137_1314_HWA - MAT 137Y Calculus Problem Set A This problem...

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MAT 137Y: Calculus! Problem Set A. This problem set is intended to help you prepare for Test #1. It is not compre- hensive: it only contains problems from some sections that were not included in past problem sets or in past tutorials. You do not need to turn in any of these problems. 1. Compute the derivative of the following functions: f ( x ) = x 9 - 9 x 3 + 2 x f ( x ) = x 2 + 2 x x 3 - x f ( x ) = 1 + x 3 x f ( x ) = x ( x + 7 3 x ) 2. In each of the following four grids we sketch the graph of a function. Sketch the graphs of their derivatives. (a) 1 2 3 4 -1 -2 -3 -4 1 2 3 -1 -2 -3 (b) 1 2 3 4 5 6 -1 -2 -3 -4 -5 1 2 3 4 -1 -2 -3 y=f(x)
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(c) 1 2 3 4 -1 -2 -3 -4 1 2 3 -1 -2 -3 (d) 1 2 3 4 5 6 -1 -2 -3 -4 -5 1 2 3 4 -1 -2 -3 y=f(x) 3. Consider the function f ( x ) = 1 x + 2 . Use the definition of derivative as a limit to compute f 0 ( - 1). 4. Consider the function g ( x ) = ( x 3 - 5 if x 2 ax + b if x < 2 where a and b are constants. What are the values of a and b that will make g differentiable everywhere?
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137_1314_HWA - MAT 137Y Calculus Problem Set A This problem...

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