Where are the inflection points The figure below gives the behavior of the deriv

Question

Where are the inflection points

The figure below gives the behavior of the derivative of g(x) on -2 le X le 2. Sketch a graph of g(x) and use your sketch to answer the following questions. 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. Where are the global maxima and minima of g on [-2, 2]? minimum at X = maximum at X = If g(- 2) = 7, 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 -4

Explanation / Answer

A. x=-1. as g"(x) =0.

B. as g'(x) >= 0 always. So g(x) is an incresing function. So

global mimina at x=-2

global maxima at x=2

C.g'(x) = [g(0) - g(-2)]/2

for some x between x=-2 & x=0. (Using LMVT)

g'(x)>0

So, [g(0) - g(-2)]/2 >0

g(0) - 7 >0

g(0) > 7

g(0)is in (7,infinity)

Since g is an incresing function with g'(x)>0

g(2)>g(0).

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