Question

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

provide your answer below:

$f(x)$ is positive over

Explanation:

Step1: Recall the concavity - second derivative relationship

If \(f''(x)>0\), the function \(y = f(x)\) is concave up.

Step2: Analyze the graph for concavity

Looking at the graph of \(y=f(x)\), we observe the intervals where the graph is concave up.

Step3: Determine the interval

From the graph, we can see that the function \(y = f(x)\) is concave up on the interval \((-1,\infty)\)

Answer:

\((-1,\infty)\)