Suppose g is a function with the second derivative g"(x)= sin(ex - 1)

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Suppose g is a function with the second derivative g"(x)= sin(e^x - 1). it is also known that g'(1)=0.

what can we conclude about the behavior of g at x=1?

a) g has a local minimum at x=1

b) g has a local maximum at x=1

c) g has a point of inflection at x=1

d) g is increasing at x=1

e) g is decreasing at x=1