REVIEW_TEST3_F15.docx

REVIEW_TEST3_F15.docx - 1 Find the points of inflection and...

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1. Find the points of inflection and discuss the concavity of the graph. 4 3 2 2 12 f x x x x

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2. Let 64 48 12 ) ( 2 3 4 x x x x f x which factors as 3 ) 4 ( ) ( x x x f . a) ) ( x f b) ) ( x f c) x-intercept of f : d) y-intercept of f : Find the following (show ALL your work) a) Critical numbers of f : b) Intervals where f is increasing : c) The relative minima are at x =
d) Intervals where f is concave up : e) The point(s) of inflection is(are) at x = f) Graph the function

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3. An open box is to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain the box with the largest possible volume? 4. Sketch the graph of the region whose area is given by the integral, and find the area using geometric formulas .
4 2 1 2 2 x dx 5. Express each limit as a definite integral. (Do not integrate the integral.) (a) 2 0 1 lim 3 n i i P i c x

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