About the Course
  • Why study maxima and minima?
Maximum and Minimum values of a function.
  • 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.
Stationary, Critical and points of Inflexion, and Concavity
  • Understanding Stationary, Critical and points of Inflexion.
  • Understanding the concept of concavity. More about points of Inflexion.
Derivative Tests for Local Maximum and Local Minimum
  • 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
Examples on maximum and minimum
  • Example1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Example 7
  • Example 8
  • Example 9
  • Example 10
Examples on First Derivative Test
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
Examples on Second Derivative Test
  • Example1
  • Example2
  • Example3
  • Example4
  • Example5
  • Example6
  • Example7
Examples on Absolute Maximum and Absolute Minimum in a closed interval
  • Example1
  • Example2
  • Example3
  • Example4
Optimization problems
  • 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 wrap-up
  • Course Summary