Chapter 4 - Applications of the Derivative - 4.4 The Shape of a Graph - Exercises - Page 194: 1

(a) C. (b) A. (c) B. (d) D.

(a) $f''(x)\lt 0$ means the function is concave down, so this is C. (b) $f''(x)$ changes from + to -, which means the function switches its behavior from concave up to concave down, so this is A. (c) $f''(x)\gt 0$ means the function is concave up, so this is B. (d) $f''(x)$ changes from - to +, which means the function switches its behavior from concave down to concave up, so this is D.