the function f is continuous for all real numbers and the graph of its derivative function f is given…

the function f is continuous for all real numbers and the graph of its derivative function f is given. determine the critical numbers of f. (use symbolic notation and fractions where needed. give your answer in the form of a comma - separated list dne if the function has no critical numbers.) the critical number(s): -3,0,1 where is f increasing? (use symbolic notation and fractions where needed. give your answers as intervals in the form (*, *). use infinity, u for combining intervals, and an appropriate type of parenthesis \(\, \)\, \\ or \\ depending on open or closed. enter ∅ if the interval is empty.)

the function f is continuous for all real numbers and the graph of its derivative function f is given. determine the critical numbers of f. (use symbolic notation and fractions where needed. give your answer in the form of a comma - separated list dne if the function has no critical numbers.) the critical number(s): -3,0,1 where is f increasing? (use symbolic notation and fractions where needed. give your answers as intervals in the form (*, *). use infinity, u for combining intervals, and an appropriate type of parenthesis \(\, \)\, \\ or \\ depending on open or closed. enter ∅ if the interval is empty.)

Answer

Explanation:

Step1: Recall increasing - function condition

A function $y = f(x)$ is increasing when $f'(x)>0$.

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

From the graph of $y = f'(x)$, we see that $f'(x)>0$ on the intervals $(-4,-2)$ and $(0,2)$.

Answer:

$(-4,-2)\cup(0,2)$