Concavity related question. From a graph of $f'(x)$, how to find on what intervals $f(x)$ is increasing or decreasing, $f'(x)$ is increasing or decreasing, on what intervals $f(x)$ is concave up or down, $f'(x)$ is concave up or down? This is the graph of $f'(x)$ !This is the graph of $f'\(x\)$ So far, what I've tried: for $f(x):$ Increasing on $(-5, -3.25)\cup (-1.5, 1)$ and Decreasing on $(-3.25, -1.5) \cup (1,6)$ for $f'(x):$ Increasing on $(-2.5, 0) \cup (3.5, 6)$ and Decreasing on $(-5, -2.5) \cup (0, 3.5)$

Concave up is where the graph looks like a smile, and concave down is where the graph looks like a frown. It looks like the graph is frowning in the interval $(-1.5,2)$, so concave down there, and smiling in $(-4.5,-1.5)$ and in $(2,5.5)$, so concave up there. When you took a picture, your book was not flat, and this distorted the graph a bit, so you take a look one more time in your book :)