# the DERIVATIVE

3. Suppose that f'(x) = x3 – 2×2 is the DERIVATIVE of f(x). Circle the correct answer and show work. (i) (3 points) The critical point x = 0 is a (A) relative max (B) relative min (c) neither Work: (ii) (3 points) The critical point x = 2 is a (A) relative max (B) relative min (c) neither Work: 4. A company makes photo frames. The cost in dollars of making x photo frames is given by C(x)= x² – 60x+ 2500 (a) (2 points) Write a function giving the average cost of making r photo frames. (b) (3 points) Using a derivative find the number of photo frames the company should produce to minimize the average cost. Confirm this with second derivative test. 5.(4 points) Use derivatives and algebra to find the inflection point of the function h(x)=-x° +7.5x² – 40x+80. Give its x and y coordinates. Show your work especially the equation you must solve and how you solve it.

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