The figure below gives the behavior of the derivative of g(x) on ?2 ? x ? 2. If

Question

The figure below gives the behavior of the derivative of g(x) on ?2 ? x ? 2.

If g(?2)=4, what are possible values for g(0)?
g(0) is in _________ ?

(Enter your answer as an interval, or union of intervals, giving the possible values. Thus if you know ?9<g(0)??4, enter (-9,-4]. Enter infinity for ?, the interval [3,3] to indicate a single point).

I found that the critical point at x=0 the maximum at x=-2 the minimum at x=2

I know that : g(2) < g(0) < g(-2)

How can I get the value of g(2) ?

Explanation / Answer

g '' (0) = 0

g ' (2) = 0

g ' (-2) = 0

g(-2) = 4

g(2) < g(0) < g(-2)

g(0) < 4

g ' (x) is symmetric about y-axis

i.e. rate of change of function is same.

g(x) is an odd function and g ' (x) is an even function

g(x) = - g(-x)

Differentiating on both sides

g ' (x) = g ' (-x)

So g(2) = -4

g(0) > -4

(-4 , 4)

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