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Derivative Review

Derivative Review. 1) Consider the function f(x) = 2x 2 + x. a. The slope of the tangent to the graph of f(x) at any point is m = ___________. b. The slope of the curve at ( 1 , 3 ) is ________________.

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Derivative Review

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  1. Derivative Review

  2. 1) Consider the function f(x) = 2x2 + x. a. The slope of the tangent to the graph of f(x) at any point is m = ___________. b. The slope of the curve at ( 1 , 3 ) is ________________. c. An equation of the tangent line at ( 1 , 3 ) is ____________________________________.

  3. 2. Find the derivative of f(x) = 8xsin2x. 3. If y = 12x3sec x tan x, compute the numerical derivative for x = 2.

  4. 8. Where does the function f(x) = x3 - 2x + 1 has horizontal tangent(s)? 9. At what point(s) does the curve defined by have vertical tangents?

  5. 10) For what value(s) of k will f(x) be differentiable if • kx2 ifx > 2 • f(x) = • 8x - 8 if x < 2 • What is the average rate of • change of f(x) over (1,3)?

  6. 14) • None (B) I only (C) II only • (D) I and II only (E) I, II, and III

  7. (A) -2.016 (B) -0.677 (C) 1.633 (D) 1.814 (E) 2.978

  8. Let f be a differentiable function with f (2) = 3 and f ' (2) = - 5, and let g be the function defined by g(x) = x f (x). Which of the following is an equation of the line tangent to the graph of g at the the point when x = 2 ?

  9. 2003 13 • Princeton Review p657 #3, 7, 8, 11,12,13,19,28..29,32,33,37,40, FR4 a,c FR6 a,c • Kaplan #4 p564,11,19,22,38*

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