Calc AB Final Exam Tri 1 FR PDF
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This document contains Calculus AB exam questions, section II, part B. The questions are free-response questions, and a graph is included to assist with some of the problems. The questions assess knowledge of the derivative, tangent lines, and the intermediate value theorem. The document is part of a higher level exam.
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CALCULUS AB SECTION II, Part B Time – 30 Questions - 2 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION. FREE RESPONSE: Show all your work and support your answers. 1. Consi...
CALCULUS AB SECTION II, Part B Time – 30 Questions - 2 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION. FREE RESPONSE: Show all your work and support your answers. 1. Consider the curve defined by 6x2 + 3xy + 2y2 +17y = 96. dy (a) Find. dx (b) Write an equation for the line tangent to the curve at the point (4,0). (c) There is a number k so that the point (3.8,k) is on the curve. Use the tangent line to approximate the actual value of k. (d) Write an equation that can be solved to find the actual value of k so that the point (3.8,k) is on the curve. (5,-2) (1,0) (4,0) (0,-1) (2,-1) (3,-2) (-1,-3) 2. The figure above shows the graph of the function f, on the closed interval 1 x 5. The graph of f has horizontal tangent lines at x = 1 and x = 3. The function f is twice differentiable with f‘(2) = -2. (a) Let g be the function defined by g(x) = x⸱f(x). Find the equation for the line tangent to the graph of g at x = 2. (b) Find the average rate of change for g(x) on the closed interval 1 x 5. (c) Use the Intermediate Value Theorem to show that g(x) = -2 on the closed interval 1 < x < 3. (d) Let h(x) be the inverse function of g(x). Find h’(-2).
