Question

the graph of f(x) is given below. on what interval(s) is the second derivative f(x) negative? give your answer in interval notation, and use commas to separate multiple intervals if necessary.

Explanation:

Step1: Recall second - derivative property

The second - derivative $f''(x)<0$ when the function $y = f(x)$ is concave down.

Step2: Analyze the graph

By observing the graph of $y = f(x)$, we look for the intervals where the curve bends downwards.
We can see that the function is concave down on the interval $(-1,1)$.

Answer:

$(-1,1)$