University:
University of Michigan
Course:
MATH 115 | Calculus I
Academic year:

2021
Views:

205

Pages:

1
Author:

whadaytumma7bdo

Math 115 / Exam 2 (November 8, 2021) page 3 2. [11 points] a. [6 points] Let f (x) be a continuous function defined for all real numbers and suppose that f ′ (x), the derivative of f (x), is given by f ′ (x) = (x − 2)(x + 3) . |x| Find the exact x-coordinates of all local minima and local maxima of f (x). If there are none of a particular type, write none. You must use calculus to find and justify your answers. Be sure your conclusions are clearly stated and that you show enough evidence to support them. Solution: The critical points of f are where f ′ (x) = 0, which occurs at x = 2 and x = −3, and where f ′ dne, which occurs at x = 0. (checking signs for 1st Derivative Test) x < −3 −3 < x < 0 0