Where is the graph of f(x) simultaneously increasing and concave down?
Ok, so I know that the answer is (-3,-2)U(1,2) but I don't know how you're supposed to get that answer. I've attached a picture of the graph.
Can someone please guide me and explain to me the process of solving this problem? Thank you!
Best Answer
$f$ is increasing $\iff$ $f'$ is positive
$f$ is concave down $\iff$ $f''$ is negative.
We don't have a picture of $f''$, but since $f''$ is the derivative of $f'$, we know that
$f''$ is negative $\iff$ $f'$ is decreasing.
Therefore, we are looking for the places where $f'$ is positive and decreasing, which you can find from the picture.