Grade 12 Calcus and vectors

( Example 2: A soup can of volume 500cm3is to be constructed. The material for the top costs 0.4 cents/cm2while the material for the bottom and sides costs 0.2 cents/cm2. Find the dimensions that will minimize the cost of producing the can )

Similar to this explain make:

-You present an optimization problem of some complexity that involves a 2-D or 3-D shape

-You define variables used to solve your problem

-an equation for a function related to your problem

-You state the domain for the x value of your function (and your reasoning behind it)

-You take the derivative of this function

-You find the critical points in order to find the maximum and minimum values for your function

-You prove that the critical points represent maximum or minimum points (eg: with an interval table)

-You find the extreme points in your function

-You analyze the extreme points and critical points to determine the optimum value that solves your problem.

-You end your problem with a concluding statement

-You find the equation of the tangent at your optimum point

-You a graph that presents: your function, the derivative and the tangent at the optimum point