Question

Suppose that f is a polynomial function. Which of the following statements is true? I. If f is increasing at x = a, then f'(a) > 0. II. If f'(a) > 0, then f is increasing at x = a. III. If f is decreasing at x = a, then f'(a) < 0. A. I only B. II only C. I and II only D. I and III only E. I, II, and III

          Suppose that f is a polynomial function. Which of the following statements is true?

I. If f is increasing at x = a, then f'(a) > 0.
II. If f'(a) > 0, then f is increasing at x = a.
III. If f is decreasing at x = a, then f'(a) < 0.

A. I only B. II only C. I and II only
D. I and III only E. I, II, and III

Suppose that f is a polynomial function. Which of the following statements is true?

I. If f is increasing at x = a, then f'(a) > 0.
II. If f'(a) > 0, then f is increasing at x = a.
III. If f is decreasing at x = a, then f'(a) < 0.

A. I only B. II only C. I and II only
D. I and III only E. I, II, and III

Added by Jordan Y.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kumareshwaran Rathinasabapathy

04/09/2022

Step 1

This is true because the derivative of a function at a point where it is increasing is positive. Show more…

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Suppose that f is a polynomial function. Which of the following statements is true? I. If f is increasing at x = a, then f'(a) > 0. II. If f'(a) > 0, then f is increasing at x = a. III. If f is decreasing at x = a, then f'(a) < 0. A. I only B. II only C. I and II only D. I and III only E. I, II, and III