The figure below gives the behavior of the derivative of \(g(x)\) on \(-2\le x\le 2\text{.}\)

*Graph of \(g'(x)\) (**not* \(g(x)\))

*(Click on the graph to get a larger version.)*

Sketch a graph of \(g(x)\) and use your sketch to answer the following questions.

*A.* Where does the graph of \(g(x)\) have inflection points?

\(x =\)

*Enter your answer as a comma-separated list of values, or enter **none* if there are none.

*B.* Where are the global maxima and minima of \(g\) on \([-2,2]\text{?}\)

minimum at \(x =\)

maximum at \(x =\)

*C.* If \(g(-2) = -8\text{,}\) what are possible values for \(g(0)\text{?}\)

\(g(0)\) is in

*(Enter your answer as an interval, or union of intervals, giving the possible values. Thus if you know \(-5 \lt g(0) \le -2\text{,}\) enter **(-5,-2]*. Enter *infinity* for \(\infty\text{,}\) the interval *[1,1]* to indicate a single point).

How is the value of \(g(2)\) related to the value of \(g(0)\text{?}\)

\(g(2)\) \(g(0)\)

*(Enter the appropriate mathematical equality or inequality, \(=\text{,}\) \(\lt \text{,}\) \(>\text{,}\) etc.)*