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165s10spec2 - Math 165 Special Assignment#2 Lowman Spring...

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Math 165 Special Assignment #2 Lowman Spring 2010 1. For some f ( x ) , f 0 ( x ) = x 2 +2 x - 8 . Find where f ( x ) is increasing and where it is decreasing. 2. For some f ( x ) , f 0 ( x ) = x 2 + 2 x - 8 . Find where f ( x ) is concave up and and where it is concave down. 3. For some f ( x ) , f 0 ( x ) = - 10 x 2 + 60 x - 50 . Find the x coordinates of all first order critical points and use the first derivative test to determine what kind of critical point at each x. 4. For some f ( x ) , f 0 ( x ) = - 10 x 2 + 60 x - 50 . Find the x coordinates of all first order critical points and use the second derivative test to determine what kind of critical point at each x. 5. Given f ( x ) = ( x 2 + 7 x + 1) · p 5 x 2 + x ) find df dx at x = 1 . 6. A company estimates that the cost in dollars of producing x units of a certain product is C ( x ) = x 2 5 + 6 x + 1000 . Find the production level that minimizes average cost. Hint: find average cost, find all critical numbers for average cost, use the first or 2nd derivative test to determine that the CNs correspond to a minimum.
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