1. Let g and h be functions defined as g(x) = 2x2 + 3x + 3 and h( x ) = =x3 + _x2 + 9. If g(x) a exists. III. f'(a) is defined. A. I only B. II only C. Ill only D. I and ill only 5. The function fis given by ((x) = 3xe-x - x - 1. Find the values of x where the graph of fis concave down. A. X2 C. X3 6. A particle is moving along a coordinate axis such that its position is defined as s( t) = 413 - 212 - 14, where t2 0. Find the rate at which the particle's position is changing at t = 3. A. 96 B. 76 C. 48 D. 30 7. When shipping a package, the sum of the base perimeter and the height cannot exceed 108 in. Find the dimensions of the package that will allow for the most volume if the base is a rectangle whose length is three times its width. A. 13.5 in x 40.5 in x 67.5 in B. 9 in x 27 in x 36 in C. 18 in x 54 in x 36 in D. 27 in x 81 in x 1 in 8. The linearization of function fat x = 3 shows that L(3.12) = 0.568. The actual value of /(3.12) is 0.554. Which of the following must be true about f? A. The function must be opening down on the interval of 3