Review problems - Review Problems for exam 2 Note these...

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Review Problems for exam 2 Note: these problems are an addition to the written homework and webwork problems. You can watch the solutions for the problems with (*) on the posted streaming power points. 1. Use implicit differentiation to find the equation of the tangent line to the curve at the given point. (a*) x 3 - y 3 = cos xy + 7 , (0 , - 2) (b) x 3 + y 3 - 9 2 xy = 0 , (2 , 1) 2*. if y = x x 2 find dy dx 3. Find the absolute maximum and absolute minimum values of the function on the given interval. (a) f ( x ) = 2 x 3 - 3 x 2 - 12 x + 1 , [ - 2 , 3] (b*) f ( x ) = xe - x , [0 , 2] 4. For a given function: find its domain, its vertical and horizontal asymptotes (if any), where it is increasing and decreasing and where it is concave up and down. Find all local maximum and minimum and all inflection points. Use this information to sketch the graph of the function. (a*) f ( x ) = 2 x - 6 x - 1 (b*) f ( x ) = x ln x (c) f ( x ) = xe x 5. Evaluate each of the following limits. (a*) lim x →∞ 9 x 6 - x x 3 + 1 (b*) lim x →-∞ 9 x 6 - x x 3 + 1 (c) lim x 1 x 7 - 1 x 3 - 1 .
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