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hello,

I have a question.

y=g(X)

domain all real number and differentiable every where

g'(-3)=g'(4)=g'(8)=0

g"(-3)=0

g"(4)=3

g"(8)=-6

whats the local extrema

I am confused

i think

Local Max is -6 at x=8

Local Min is 3 at x=4

but what does g'(-3)=g'(4)=g'(8)=0 means then.

Thanks

Mnsor

If f'(x) = 0, the point is a maximum, minimum, or inflection points.

If f"(x) > 0, f(x) is a local minimum. If f"(x) < 0, f(x) is a local maximum.

If f"(x) = 0, there is an inflection point in f() at x.

Since g'(-3) = 0, g'(4) = 0, and g'8) = 0, x=-3, x=4, and x=8 are all critical points.

Since g"(-3) = 0, that means there is an inflection point in g(x) at x = -3.

Since g"(4) = 3, and 3>0, that means there is a minimum in g(x) at x = 4.

Since g"(8) = -6, and -6<0, that means there is a maximum in g(x) at x = 8.

The values of g(x) at any of these points are not given.

Differential Equations

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