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Quiz 8 (Prequiz) - Functions III (Product and Quotient Rules)

# Quiz 8 (Prequiz) - Functions III (Product and Quotient Rules)

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Unformatted text preview: AP Calculus AB PreQuiz 8 Derivatives III (Product and Quotient Rules) Objectives: You will be able to calculate the derivative of a function using the product rule You will be able to calculate the derivative of a function using the quotient rule Name___________________________________ Date ________________________ MULTIPLE CHOICE. Choose the one alternative that Find the indicated derivative of the function. best completes the statement or answers the question. (x - 6)(x2 + 4x) dy . 3) Find if y = dx x3 Find y . 10 48 - A) 1) y = (5x - 2)(5x3 - x2 + 1) x2 x 3 A) 100x3 - 15x2 + 45x + 5 48 B) 48 + B) 75x3 + 45x2 - 15x + 5 x C) 100x3 - 45x2 + 4x + 5 D) 25x3 + 15x2 - 45x + 5 C) 2 48 + x2 x 3 48 48 - x2 x 3 D) x - Use the quotient rule to find the derivative. x3 2) y = x - 1 A) y = B) y = C) y = D) y = -2x3 + 3x 2 (x - 1)2 2x3 - 3x 2 (x - 1)2 2x3 + 3x 2 (x - 1)2 -2x3 - 3x 2 (x - 1)2 Solve the problem. 4) Find the tangent to the curve y = point (1, 3). A) y = x + 3 B) y = 3x C) y = 3 D) y = 0 6x at the x2 + 1 1 5) The curve y = ax2 + bx + c passes through the point (2, 30) and is tangent to the line y = 3x at the origin. Find a, b, and c. A) a = 0, b = 6, c = 3 B) a = 3, b = 0, c = 6 C) a = 6, b = 3, c = 0 D) a = 7, b = 0, c = 0 Find dy/dx. 8) y = 7x2 + x - 1 x3 - 6x2 -7x4 - 3x3 + 15x2 - 12x (x3 - 6x2 ) 2 35x4 - 168x3 + 9x2 - 12x (x3 - 6x2 ) 2 -7x4 - 2x3 + 9x2 - 12x (x3 - 6x2 ) 2 35x4 - 2x3 + 9x2 - 12x x3 - 6x2 A) B) C) D) Suppose u and v are differentiable functions of x. Use the given values of the functions and their derivatives to find the value of the indicated derivative. 6) u(1) = 3, u (1) = -5, v(1) = 7, v (1) = -4. d (uv) at x = 1 dx A) 23 B) -43 C) -47 D) 47 9) y = (x2 - 4x + 2)(4x3 - x2 + 4) A) 4x4 - 64x3 + 36x2 + 4x - 16 B) 20x4 - 68x3 + 36x2 + 4x - 16 C) 20x4 - 64x3 + 36x2 + 4x - 16 D) 4x4 - 68x3 + 36x2 + 4x - 16 7) u(1) = 5, u (1) = -5, v(1) = 6, v (1) = -2. d v at x = 1 dx u A) 4 B) - C) - D) 4 5 8 5 4 5 2 Answer Key Testname: QUIZ 8 (PREQUIZ) FUNCTIONS III (PRODUCT AND QUOTIENT RULES) 1) 2) 3) 4) 5) 6) 7) 8) 9) C B C C C C D C B 3 ...
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