1. The Derivative Obj: Students will be able to notate and evaluate derivatives

2. The Derivative: It is the slope of the tangent at any x-value It is the INSTANTANEOUS slope of a point The derivative of a function IS a function f’(x) whose value at x is

3. Alternate Definition The derivative of a function f at the point x = a is

4. Example: Slope at a point Find the slope of the function f(x) = 2x 2 + 3x at the point (-2, 2)

5. Example Find f’(x) for f(x) = 2x 2

6. Treating f’(x) as a function You can use the derivative function to find the slope at ANY point on f(x) Ex: Find the slope at x=3 for f(x) = 2x 2 Ex: Find the slope at x= 6 for f(x) = 2x 2

7. Example Con’t.d Ex: Find the slope at x= 6 for f(x) = 3x 2 + x

8. Notations NotationHow to read F’(x)“f prime of x” Y’“y prime” dy/dx “dy dx” “the derivative of y with respect to x” df/dx “df dx” “the derivative of f with respect to x” d/dx f(x) “d dx of f at x” “The derivative of f at x”

9. HOMEWORK PP. 105-106 {1-3, 5-12, 17, 18}