analyze the following graph of $f(x)$. select all of the intervals over which the function $f(x)$ is concave…

analyze the following graph of $f(x)$. select all of the intervals over which the function $f(x)$ is concave up.\nselect all that apply:\n$(-\\infty,0)$\n$(0,\\frac{1}{2})$\n$(\\frac{1}{2},\\infty)$\nnone of the above.

analyze the following graph of $f(x)$. select all of the intervals over which the function $f(x)$ is concave up.\nselect all that apply:\n$(-\\infty,0)$\n$(0,\\frac{1}{2})$\n$(\\frac{1}{2},\\infty)$\nnone of the above.

Answer

Explanation:

Step1: Recall the concavity rule

A function (y = f(x)) is concave up when (f''(x)>0). Since (f''(x)) is the derivative of (f'(x)), we need to find where (f'(x)) is increasing.

Step2: Analyze the graph of (f'(x))

Looking at the graph of (y = f'(x)), we observe the slope of (f'(x)). The slope of (f'(x)) (which is (f''(x))) is negative everywhere on the given graph.

Answer:

None of the above.