A function $f$ is defined for $-4\le x\le 3$. The graph of $f$ is given below. The graph of $f$ has a local maximum when $x = 0$, and a local minima when $x = -3$ and $x = 2$.
a) Write down the $x$-intercepts of the graph of the derivative function, $f’$.
Since there are minimums and maximums on the first graph, I know that these are found by setting the derivative to 0, which would make these on the $x$-intercept. I got: $x = -3, x = 0, x = 2$.
b) Write down all values of $x$ for which $f’(x)$ is positive.
Since it concave up at $x = -3$ and $x = 2$ on the original graph, would this be our values?
c) At point $D$ on the graph of $f$, the $x$-coordinate is $-0.5$ Explain why $f’’(x) < 0$ at $D$.
Because it’s concave down? I’m not sure how else to explain it.