Applications of Differentiation – Maximum  and Minimum Optimization Problems

Applications of Differentiation – Maximum and Minimum Optimization Problems

Learning Objectives:

Understand Applications of Differentiation – Maximum/Minimum/Optimization Problems

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:

 

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.

 

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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