if the derivative of f is f'(x)=ln(x^2+1)-2, at which of the following values of x does f have an abslolute value?

a)2.53
b)0
c)2.72
d)4.44
e)1.72

I assume you mean absolute max or min.

That would occur where f'(x) = 0

So, when does ln(x^2+1)-2=0?
ln(x^1+1) = 2
x^2 + 1 = e^2
. . .