Multiple choice

Questions: there are 6 calculation-type questions and 3 true-false questions. 1. Find the minimum value of f(x) = ' - 8x3 + 22x2 - 24x + 2, where x is in [0,4) and the value of x where it occurs (A) -7;1 and 3 (B) -6;1 (C) -7;3 (D) -6;1 and 3 (E) None of (A) - (D) 2 For the same function as in Question 1, the maximum value of it and the point where it occurs is (A) 2;0 (B) 0;4 (C) 2;4 (D) 0;0 (E) None of (A) - (D) 3. Assume the price of a product in t years is given by the function f(t) = 2000 - 10tes , what is the minimum price of the product and when does it occur? (A) 2000,0 (B) 199.66,2 (C) 1999.94, 10 (D) 198.66, 1 (E) None of (A) - (D) 4. Find the indefinite integral: f (6et - r3(vz + 1)) dx (A) 6ex? 2x2 -*+C (B) 6et - x4 - x3+ C (C) 6et - mi-r + C 5. Find the indefinite integral:S ( #7 -1) de (A) 3 +1-523 + C (B) 20x1 3 +x-5x3+C (C) 20 + -5x + C (D) 2013 3 +x-5ri+ C (E) None of (A) - (D) 6. If f"(x) =30x4 + 12r and f'(1) = 10, evaluate f(2) - f(-2) (A) 40 (B) 24 (C) 8 (D) 32 (E) None of (A) - (D) 7. 0 for incorrect answers or no answer Answer "True" or "False" for the following three parts: (i) If f'(a) does not exist, then f has a relative extremum at a. (ii) An inflection point is a point where the function changes from being concave upward to being concave downward