1. 3.1 The Derivative Tues Sept 22 If f(x) = 2x^2 - 3, find the slope between the x values of 1 and 4

2. Test Review Retakes this week

3. Recall, it is difficult to find the slope of a function at a particular point. The Slope Problem

4. The Derivative at a point The derivative of a function f(x) at x = a is defined as: We can now find the equation of tangent lines at specific points

5. Ex 1 Find an equation of the tangent line to the graph of f(x) = x^2 at x = 5

6. Ex 2 Find the derivative of at x = 3

7. Ex 3 Find the tangent line of f(x) = 1/x at x = 2

8. The Derivative at a point With a calculator: MATH -> nDeriv Function, x, x-value OR Graph -> 2 nd -> Calc -> dy/dx -> type in x value

9. The derivative of a function The derivative of f(x) is the function f’(x): Lots of simplification will be involved!

10. Ex 1 Find the derivative of

11. Ex 2 Find the derivative of f(x) = 2x^2 - 5x + 7

12. Ex 3 Find the derivative of y = x^-2

13. Closure Journal Entry: How do we use limits to find the slope of the tangent line to a curve? HW: 3.1 p.126 #2, 5, 9, 11, 14, 33, 41, 47, 53 3.2 p.139 #1 3 5