Learning Objectives:

__Applications of Differentiation Maximum/Minimum/Optimization Problems__

*Some important differentiation applications are:*

*A) **Max/Min Problems:*

1. Determine maximum area of a garden.

2. Find the maximum/Minimum volume of a box.

3. Determine the dimensions of a rectangle bounded by the semicircle.

4. Determine the minimum inventory cost.

5. Determine the maximum profit.

6. Maximize the area of three identical corrals.

7. Minimize the cost of a fenced area.

*B)Optimization function:*

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1. Maximize a Crop Yield.

2. Determine maximum area of a rectangle inscribed by a parabola.

3. Minimization of the surface area of an open Top Box.

4. Find the dimensions for a can that will minimize production cost.

5. Maximize the area of a normal window.

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*C)Cost Function Application:*

1.Find the average cost function and minimize the average cost.

2.Determine marginal cost,Average cost minimum average cost.

3.Find a demand function and a rebate amount to maximize revenue and profit.

4.Find the cost and demand functions and maximize profit.

**Hook Question:**

*1. **State some applications of differentiation regarding **Maximum, Minimum and Optimization problems.*

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