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Unformatted text preview: Name: TA: Math 10A. Midterm Exam 2 November 17, 2009 Sec. No: PID: Sec. Time: Turn off and put away your cell phone. You may use any type of calculator, but no other electronic devices during this exam. You may use one page of notes, but no books or other assistance during this exam. You may leave answers in symbolic form, for example 42 or ln(6). Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. # 1 2 3 4 5 Points 4 4 4 6 6 24 Score 1. (4 points) Use the graph of f below to determine which is larger in each of the following pairs:
y = f(x) y x 0 1 2 3 4 (a) f (1) or f (3)? (b) the average rate of change of f between x = 0 and x = 2 or between x = 1 and x = 3? (c) f (1) or f (2)? (d) lim f (3 + h)  f (3) f (1 + h)  f (1) or lim ? h0 h0 h h 2. (4 points) Use the graph of f below to complete the following table with the signs of f and f at the points A and B. In each of the empty squares, write either > 0, < 0, or = 0. y y = f(x) B 0 A x A B f <0 >0 f f 3. (4 points) Suppose that f is a function with f (5) = 2, f (5) = 7 and f (5) = 9. (a) Find an equation for the tangent line to the graph of f at the point (5, 2). (b) Is the graph of f concave up or concave down at the point (5, 2)? Briefly justify your answer. 4. (6 points) Find the derivative of the given function. Assume that a is a fixed constant. (a) f (x) = 4 sin(x)  9 x (b) g(x) = ax cos(2x + 1) (c) h(x) = x7  ax3 ex + 1 5. (6 points) Consider the functions f and g whose graphs are given below.
y 6 y = f(x) 5 4 3 2 y = g(x) 1 x 0 1 2 3 4 5 (a) If h(x) = f (x) g(x), what is h (1)? Please show your work. (b) If m(x) = f (g(x)), what is m (3)? Please show your work. (c) List all values of x at which g is not differentiable. ...
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This note was uploaded on 05/28/2010 for the course MATH 3412341 taught by Professor Staff during the Spring '06 term at UCSD.
 Spring '06
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