# R h volume π r 2 h bottom π r 2 side wall 2 π rh

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r h Volume = π r 2 h Bottom = π r 2 Side wall = 2 π rh

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CALCULUS I, TEST IV 6 Problem 3 [12 points] An object moves along a straight line with acceleration a ( t ) = 12 t - 4 . Use antiderivatives to answer the following questions. (a) Find the velocity function v ( t ) of the object if its initial velocity is v (0) = 3. (b) Find the position function s ( t ) of the object if its initial position is s (0) = 0.
CALCULUS I, TEST IV 7 Problem 4 [22 points] Consider the function f given by f ( x ) = x 2 x 2 - 4 . Answer all the following questions. (a) Find the x and y -intercept(s) of the curve. (b) Find, if any, the vertical and horizontal asymptote(s) of the curve. (c) Find the interval(s) of increase, and the interval(s) of decrease. (d) Find, if any, all local maximum and local minimum value(s). [Be sure to give both x and y -coordinates!]

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CALCULUS I, TEST IV 8 (e) Find interval(s) where the function is concave down, and interval(s) where it is concave up. [Hint: Factoring out might prove useful in your calculations!] (f) Find inflection points (if any). (g) Use the information from parts (a)–(f) above to sketch the graph.
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