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Detailed course in maxima and minima to gain confidence in problem solving. – Free Course

(1) About the Course

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(2) Maximum and Minimum values of a function.

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(3) Stationary, Critical and points of Inflexion, and Concavity

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(4) Derivative Tests for Local Maximum and Local Minimum

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(5) Examples on maximum and minimum

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(6) Examples on First Derivative Test

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(7) Examples on Second Derivative Test

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(8) Examples on Absolute Maximum and Absolute Minimum in a closed interval

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(9) Optimization problems

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

(10) Course wrap-up

  • Why study maxima and minima?
  • Understanding maximum and minimum .
  • Understanding Local Maximum and Local Minimum
  • Understanding Global Maximum and Global Minimum
  • Understanding Absolute Maximum and Absolute Minimum in a closed interval.
  • Understanding the behavior of f ‘(x) at Local Maxima and Local Minima.
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
  • Understanding First Derivative Test for Local Maximum and Local Minimum.
  • Understanding Second Order Derivative Test for Local Maximum and Local Minimum
  • Understanding Higher Order Derivative Test for Local Maximum and Local Minimu
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
  • Example1
  • Example2
  • Example3
  • Example4
  • About optimization
  • Example1_Square has the largest area
  • Example2_ Square has the smallest perimeter
  • Example3_ Maximum volume of the open box
  • Example4_ Rectangle is a square of maximum area inscribed in a circle
  • Example5_ Height of a closed cylinder of maximum volume is equal to the diameter
  • Example6_Minimise the combined area of the square and the circle cut from a wire
  • Example7_ To maximise the product ( x^ 2 )(y^5 ) , x and y are positive numbers
  • Example8_Minimise total surface area of right circular cylinder, given volume
  • Example9_ Area right triangle maximum when isosceles and hypotenuse given
  • Course Summary

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