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April 7, 2016

**MCV4U (Calculus & Vectors):**

**How do I solve Derivative Application problems?**

**Type 1: Minimum and Maximum problems**

**Examples**: greatest profit, least cost, least time, greatest voltage, optimum size, least size, greatest strength, and greatest distance.

**Steps:**

1) When feasible, draw a diagram.

2) Define variables to the given quantities and quantities to be determined.

3) Write a primary equation for the quantity that to be maximized or minimized.

4) write a secondary equation for the given quantity.

5) Solve for one of the variables from the secondary equation.

6) Substitute into the primary equation so that primary equation has only one variable.

7) Determine the restrictions of the primary equation (domain). That is, determine which value make sense for the given problem.

8) Find the derivative of the NEW primary equation, set it equal to 0 and solve for the variable. We know maximum/minimum occur when derivative is zero.

9) Solve for other variable using the secondary equation.

10) Confirm if it is max/min by doing the second derivative test or first derivative test. If y''(c) >0, it is a min; If y ''(c) <0, it is a max; If y'' (c) = 0, test fails. In this case, use the first derivative test. Note that c is the critical number from the first derivative y ' = 0.

Stay tuned for Type 2: Related Rates.....

**By Mrs. Uma Gnanaharan**

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**MPM1D, MPM2D, MCR3U, MCF3M, MHF4U and MCV4U: **

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**Click here to get the Math Reference sheet.**

**Click here to get the factoring practice January 2015. **

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