Unformatted text preview: Calculus 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. Solve the problem. d 8) Find (x2  6). Find the derivative. dx 1) g(x) = 24x  15 9) Find 2) f(x) = (2x  4)(3x + 1) (Hint: Expand function first.) d (2x2 + 9). dx 3) f(x) = 5x2  2x  3 10) If y = x2  1, find an equation of the tangent line to the graph of y at x =4. Use the definition to find the functions derivative. Then evaluate the derivative at the indicated point. 8 4) f(x) = , f (1) x 11) Find an equation of the tangent line to the graph of y = x2  x, at the point (4, 20). 5) f(x) = x2 + 7x  2, f (0) 12) Find an equation of the tangent line to the graph of y = 8 x  x + 3 at the point (64, 3). 6) g(x) = 3x 2  4x, g (3) 7) f(x) = 5x + 9, f (2) 1 Find the values of x where the function is not differentiable. 13) 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. 17) y = 5 x + 8, at x = 0 18) y = 3 , at x = 5 x + 5 14) 3 19) y = 7  x, at x = 0 20) y = 3 x + 7 , at x = 7 15) Determine the values of x for which the function is differentiable. 21) y = 3x + 9 22) y = 16) 1 x2  4 23) y = x  7 2 Answer Key Testname: QUIZ 6 (PREQUIZ) DERIVATIVES I 1) 24 2) 12x  10 3) 10x  2 4) f (x) =  5) 6) 7) 8) 9) 10) 11) 8 ; f (1) = 8 x2 f (x) = 2x + 7; f (0) = 7 g (x) = 6x  4; g (3) = 14 f (x) = 5; f (2) = 5 2x 4x y = 8x  17 y = 9x  16 1 12) y =  x + 35 2 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) x = 2, x = 2 Exists at all points x = 2 x = 0, x = 3 corner discontinuity vertical tangent cusp All reals All reals except 2 and 2 All reals greater than 7 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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