Chapter 4 - Section 4.3 - How Derivatives Affect the Shape of a Graph - 4.3 Exercises - Page 301: 24

a) $f'(x)<0$ and $f''(x)<0$ for all $x$. b) $f'(x)>0$ and $f''(x)>0$ for all $x$.

(a) The function is decreasing, so $f'(x)<0$, and the function is concave down, so $f''(x)<0$. (b) For this function, it is increasing, so $f'(x)>0$, and it is concave up so $f''(x)>0$.