Chapter 3 - Applications of Differentiation - 3.3 How Derivatives Affect the Shape of a Graph - 3.3 Exercises - Page 228: 21

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a) Because $f'(x) \gt 0$ and $f''(x) \lt 0$ for all $x$, the function must be always increasing (since the first derivative is always positive) and concave downward (since the second derivative is always negative) b) Because $f'(x) \lt 0$ and $f''(x) \gt 0$ for all $x$ the function must be always decreasing (since the first derivative is always negative) and concave upward (since the second derivative is always positive)