Tuesday, October 24 Lesson 3.1 Score 2.8

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Presentation transcript:

Tuesday, October 24 Lesson 3.1 Score 2.8 “When you have exhausted all possibilities, remember this ~ YOU HAVEN’T.” Thomas Edison Lesson 3.1 The formal definition of the derivative Score 2.8

3.1 The Derivative of a function

Review: Secant line versus Tangent line The slope of the tangent line at x = a is called the Derivative of the function f ’(a). “ f prime at a”

When the limit exists, we say that the function is differentiable at a. As point Q gets closer to point P, then h gets closer to zero.

As point Q gets closer to point P, then x gets closer to a.

The equation of a line: 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 ) The equation of a line tangent to a curve at the point (a, f (a) ): 𝑦−𝑓 𝑎 = 𝑓 ′ 𝑎 𝑥−𝑎 Or 𝑦=𝑓 𝑎 +𝑓′(𝑎)(𝑥−𝑎)

Lesson 3.1 Scoring Guidelines 5 Limit done both ways 7 Slope of secant; is it larger or smaller than f’(2)? 9 Estimate f’(1) and f’(2) 13 Which is larger? 19 Find derivative; then write equation of tangent line 35 Find derivative using limit process 49 Intervals on which derivative is positive 51 Find f(x) and a 56 59 A. B.