Find the maximum and minimum value of f(x)=4x^3 -18x^2+27x -7
there is no global maximum or minimum, since odd-degree polynomials go to infinity in both directions. There are local extrema, however, where
f'(x) = 0
That is, solve
4x^2 - 12x + 9 = 0
You will find that there is only one extremum, so that means there is no local max or min, but only a point of inflection. Trick question!