Question

Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = −3, x = 1, and x = 2. There are horizontal tangents at x = −1.5 and x = 1.5. Which of the following statements is true?

Answer 1

Answer `A` is correct. We can immediately see it's true.

Recall that a function is concave down if the second derivative is negative, an that a function is decreasing if it's first derivative is negative.

We can see that the derivative `f'` is decreasing on `[-1.5, 1.5]`. This means that the first derivative of the first derivative, or the second derivative of `f`, is negative, which in turn means that the function is concave down on `[-1.5, 1.5]`.

Hopefully this helps!