Aim: Curve Sketching Do Now: Worksheet Aim: Curve Sketching.

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Presentation transcript:

Aim: Curve Sketching Do Now: Worksheet

Aim: Curve Sketching

Find any points of inflection of f(x)

Aim: Curve Sketching You may use your calculator

Aim: Curve Sketching You may use your calculator

Aim: Curve Sketching You may use your calculator

Aim: Curve Sketching

Aim: Optimization Optimization involves finding the largest or smallest values of a function, such as area, perimeter, volume or time. Typical Optimization Problems:  How large a rectangular area can be enclosed with a fixed amount of fencing?  What is the largest volume that can be enclosed by making a box from a rectangular piece of material?  What is the minimum distance from a given point to a curve?

Aim: Optimization A rectangular vegetable garden is to be enclosed by 60 feet of fencing. Find the length and width that will give the maximum area.

Aim: Optimization Find the critical points of the derivative of the area function.

Aim: Optimization A rectangular vegetable garden is to be enclosed using the wall of a building as one side and 60 feet of fencing on the other three sides. Find the length and width that will give the maximum area.

Aim: Optimization

Aim: Curve Sketching