## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# Chapter 4 - Section 4.3 - How Derivatives Affect the Shape of a Graph - 4.3 Exercises: 34

#### Answer

(a) Point B (b) Point E (c) Point A

#### Work Step by Step

(a) $\frac{dy}{dx}=f'\gt0$. This means that $f$ is increasing at this point. We can eliminate points A, E (where graph $f$ is decreasing) and D (where graph $f$ is neither increasing nor decreasing). $\frac{d^2y}{dx^2}=f''\gt0$. This means $f$ is concave upward. This leads us to pick the point B, since $f$ is concave upward at B. (b) $\frac{dy}{dx}=f'\lt0$. This means that $f$ is decreasing at this point. We can eliminate points B, C (where graph $f$ is increasing) and D (where graph $f$ is neither increasing nor decreasing). $\frac{d^2y}{dx^2}=f''\lt0$. This means $f$ is concave downward. This leads us to pick the point E, since $f$ is concave downward at E. (c) $\frac{dy}{dx}=f'\lt0$. This means that $f$ is decreasing at this point. We can eliminate points B, C (where graph $f$ is increasing) and D (where graph $f$ is neither increasing nor decreasing). $\frac{d^2y}{dx^2}=f''\gt0$. This means $f$ is concave upward. This leads us to pick the point A, since $f$ is concave upward at A.

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