1. Calculus 4.1: Connecting f, f’, and f” A. Remember these relationships!! 1. fINCDEC local max local min f’ + – pos  neg neg  pos 2. fCON UP CON DOWN P.O.I f’ INC DEClocal max/min f” + – changes sign

2. B. Sketching Curves 1. Study picture table on p. 213!! 2. Examples a. Stewart text p.244 (EX 5) b. PH text p.212 (EX 8) c. PH text p.214 (exploration 2)

3. Calculus 4.2: Optimization Problems A. Strategy for solving max/min problems: 1. Understand the problem 2. Develop a mathematical model 3. Graph the function 4. Identify critical points and endpoints 5. Solve the mathematical model 6. Interpret the solution

4. B. Optimization Problems – Economics 1. Maximum Profit occurs at the production level at which marginal revenue equals marginal cost. see fig 4.42 p.223 2. Minimizing Average Cost – the production level at which average cost is smallest is a level at which average cost equals marginal cost.

5. Calculus 4.3: Linear Approximation & Differentials A. If f is differentiable at x=a, then the equation of the tangent line defines the linearization of f at a. B. The approximation is the standard linear approximation of f at a. C. The point x=a is the center of the approximation.

6. D. Differentials 1. Let y = f(x) be a differentiable function. The differential dx is an independent variable. The differential dy is dy = f’(x)dx 2. Estimating Change: Let f(x) be differentiable at x=a. The approximate change in the value of f when x changes from a to (a+dx) is df = f’(a)dx

7. Calculus 4.4: Related Rates A. Strategy: 1. Read the problem carefully 2. Draw a diagram if possible 3. Assign variables to all quantities that are functions of time 4. Write an equation relating the quantities in the problem 5. Use the Chain Rule to differentiate both sides with respect to t 6. Substitute the given info into the resulting equation and solve for the unknown rate

8. Calculus Unit 4 Test  Grademaster #1-25 (Name, Date, Subject, Period, Test Copy #)  Do Not Write on Test! Show All Work on Scratch Paper!  Label BONUS QUESTIONS Clearly on Notebook Paper. (If you have time)  Find Something QUIET To Do When Finished!