# PART 1 For each multiple choice problem circle only one

Last updated: 12/8/2023

PART 1 For each multiple choice problem circle only one answer There is no partial credit for multiple choice problems 1 5 points Which of the following is a critical point of the function f x ln x 8x fx In x 8x A x 1 16 B 16 x 1 4 D x 4 E f x has no critical points 2 5 points A function f t has a local minimum at t 2 and a local maximum at t 4 Assuming t 2 and t 4 are critical points found by setting f t 0 and solving for t which of the following must be true Af 2 is positive and f 4 is positive B f 2 is positive and f 4 is negative C f 2 is negative and f 4 is negative D f 2 is negative and f 4 is positive t 2 210 max t 9 9 0 4 4 20 242 0 3 5 points Below is table of values for the second derivative of a smooth continuous function g x If x 3 and x 1 are the only candidates for where the original function g x may have an inflection point what can we conclude X 4 g x 2 3 0 1 2 0 4 0 20 A g x has an inflection point at both x 3 and x 1 B g x has an inflection point at x 3 but not at x 1 C g x has an inflection point at x 1 but not at x 3 D g x has no inflection points