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BC 1 Problem Set #5 Spring 2014 Name Due Date: Monday 31 Mar. (at beginning of class) Extra credit if turned in 10 day early Please show appropriate work – no big calculator leaps – except as indicated. Work should be shown clearly, using correct mathematical notation. Please show enough work on all problems (unless specified otherwise) so that others could follow your work and do a similar problem without help. Collaboration is encouraged, but in the end, the work should be your own. 1. Differentiate the following function. Don’t even think of simplifying or using the TI-89! f ( x) 2. sin 4 x3 x2 2 x ln 3 x 2 Suppose f x2 2 x h x , f (0) 4, f (4) 2, f (8) 3, f 0 3, f 2 3, f 4 5, f 6 7, f ( x) and f 8 2 . Determine the value of h 4 , if possible, showing your work. BC 1 Problem Set #5 Spring 2014 3. Suppose (1) = 0 and that is the function graphed at the right. If Name Due Date: Monday 31 Mar. (at beginning of class) Extra credit if turned in 10 day early Graph of G x x , is G concave up 5 or concave down at x = –4? Justify your answer. 4. Find all points (a, b) on the graph of f ( x) 2e x such that the tangent line to f at goes through the point (1, 0) . 2 BC 1 Problem Set #5 Spring 2014 5. Name Due Date: Monday 31 Mar. (at beginning of class) Extra credit if turned in 10 day early Let h x g x . Use the graphs of f and g below to estimate the values of x where the graph of h has stationary points. (That is, estimate all values of x such that h( x) 0 ). y = f(x) y = g(x)