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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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