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Unformatted text preview: AP Calculus AB PreQuiz 6  Derivatives I
Name___________________________________ Date: ___________________ Objectives: You will be able to calculate the derivative of a function using the original and the alternative form of the derivative. You will be able to determine if a function is differentiable. You will be able to apply the relationship between differentiability and continuity. 7) g(x) = x3 + 5x; g (1) Find the derivative. 1) f(x) = (6x  3)(6x + 1) (Hint: Expand function first.) Solve the problem. d 8) Find (4x2 + 9). dx 2) g(x) = 3  9x3 3) f(x) = 5x2  6x + 9 9) If y = x2  3, find an equation of the tangent line to the graph of y at x =2. Use the definition to find the functions derivative. Then evaluate the derivative at the indicated point. 8 4) f(x) = , f (1) x 10) Find an equation of the tangent line to the graph of y = x2  x, at the point (3, 12). 5) f(x) = x2 + 7x  2, f (0) 11) Find an equation of the tangent line to the graph of y = 2 x  x + 7 at the point (4, 7). 6) g(x) = 3x 2  4x, g (3) 1 Find the values of x where the function is not differentiable. 12) If the function is not differentiable at the given value of x, tell whether the problem is a corner, cusp, vertical tangent, or a discontinuity. 16) y = 7 x + 1, at x = 0 17) y = 3 , at x = 2 x + 2 13) 3 18) y = 2  x, at x = 0 19) y = 3 x + 12 , at x = 12 14) Determine the values of x for which the function is differentiable. 20) y = 3x  5 21) y = 15) 1 x2  25 22) y = x  4 2 Answer Key Testname: QUIZ 6 (PREQUIZ) DERIVATIVES I 1) 72x  12 2) 27x2 3) 10x  6 4) f (x) =  8 x2 ; f (1) = 8 5) f (x) = 2x + 7; f (0) = 7 6) g (x) = 6x  4; g (3) = 14 7) g (x) = 3x 2 + 5; g (1) = 8 8) 8x 9) y = 4x  7 10) y = 7x  9 1 11) y =  x + 9 2 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) x = 2, x = 2 Exists at all points x = 2 x = 0, x = 3 corner discontinuity vertical tangent cusp All reals All reals except 5 and 5 All reals greater than 4 3 ...
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This note was uploaded on 02/03/2012 for the course MATH 101 taught by Professor Lee during the Spring '11 term at International Institute for Higher Education.
 Spring '11
 Lee
 Derivative

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