Math201420OldTest#2 - x x f 6 Let 1 3 2 3 3 = cx bx ax x Q...

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Math 141 Old Test #2 1. Find an equation of the tangent line to the graph of 1 1 ) ( - = x x f at the point (3, ½) . 2. If 10 12 6 ) ( 2 + + = x x x f , find ) ( 4 x f . 3. Make a conjecture about the derivative by calculating the first few derivatives and observing the resulting pattern. a. y = sinx find the 87 th derivative of this function. b. y = xcosx find the 17 th derivative of this function. 4. A particle moves along the x-axis , its position at time, t given by 2 1 ) ( t t t x + = , 0 t where t is measured in seconds and x is in meters. a. Find the velocity at time, t. b. Find the acceleration at time, t. 5. Show, using the definition of the derivative of a function, that if 5 2 ) ( 2 + - = x x x f , then 2 2 ) ( - =
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Unformatted text preview: x x f 6. Let 1 3 2 3 ) ( 3--+ = cx bx ax x Q . If (0, -1) is an inflection point and (1,2) is a relative extremum, find the values of a, b, and c. 7. Find the derivative of xy ye x = + 2 . 8. Find the derivative of x x y ) 3 ( + = using logarithmic differentiation. 9. Given the graph of the derivative of H, find: a. When H is increasing . (Justify your answer!) b. The intervals where H is concave up. (Justify your answer) c. Sketch a graph of what H could like. 10. Use the graph given, ( I’ll put it on the board), determine all the x-values at which the function is not differentiable....
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