Definition
The process that is used to calculate the maximum or minimum value for a function. This may be global (all x values) or for a given domain (set of x values).
1) Determine the function. This may be given in the question or determined from the information in the question. The Constraint is substituted into the function to give a function with only one variable.
2) Differentiate the function to find the rate of change or gradient function.
3) Make the derivative equal zero and solve to find the x co-ordinate of the stationary points.
4) Determine the nature of the stationary points by finding the gradient either side of the stationary points.
This can be done by randomly selecting a x value to the left and right of the S.P. and substituting into the gradient function. Refer to Stationary Points for more.
5) Substitute the x value of the S.P. into the original function to calculate the y value.
2) Differentiate the function to find the rate of change or gradient function.
3) Make the derivative equal zero and solve to find the x co-ordinate of the stationary points.
4) Determine the nature of the stationary points by finding the gradient either side of the stationary points.
This can be done by randomly selecting a x value to the left and right of the S.P. and substituting into the gradient function. Refer to Stationary Points for more.
5) Substitute the x value of the S.P. into the original function to calculate the y value.
Class Examples (function given)
Class Examples (word problems)
More Examples
Find the dimensions of a rectangle with area 1000m2 whose perimeter is as small as possible.
https://www.youtube.com/watch?v=Zq7g1nc2MJ8
Find the max volume of a box. (Measurements in feet)
https://www.youtube.com/watch?v=_oS_LjKse38
https://www.youtube.com/watch?v=Zq7g1nc2MJ8
Find the max volume of a box. (Measurements in feet)
https://www.youtube.com/watch?v=_oS_LjKse38