Determine whether the following statements are true and give

Last updated: 7/19/2022

Determine whether the following statements are true and give an explanation or counterexample. a. The zeroes of f' are - 3, 1, and 4, so the local extrema are located at these points. Choose the correct answer below. A. False. The zeros of f' are the inflection points of f. B. True. The zeros of f' are the local extrema of f. C. True. The zeros of f' are local extrema so long as the denominator is nonzero at those points. D. False. A zero of f' is a critical point and is a local extremum so long as it is in the domain of f(x) and f'(x) changes sign. Take, for example, the function f(x) = (x+3)³(x - 1)³(x-4)³.