Question

For what values of x does the graph of g have a point of inflection

Answer 1

The points of inflection are the points where the 2nd derivative is 0.
or in other words, where the function changes concavity.

Answer 2

Take the derivative of g(x) you get f(x)
so g'(x) = f(x)
and g '' (x) = f'(x).

So if you take 1st derivative of f(x) and find where it's 0. That's the point of inflection on the 2nd derivative of g(x).
Seems to me that it's the max at 2 and min at 5.

Answer 3

ok but don't I have to evaluate that integral
g ' (x)=f (x)
g " (x)= f ' (x)

Answer 4

yes, you want g'' = 0
which means f' = 0
which occurs at x=2 and x=5

Answer 5

thanks everyone