Point of inflection

Problem:



Solution:

The point of inflection is where the second derivative is 0, so we compute the second derivative as follow:

$ f'(x) = -3x^2 + 18x - 4 $
$ f''(x) = -6x + 18 $

Therefore the point of inflection has x coordinate 3, the y coordinate is $ -(3)^3 + 9 \times 3^2 - 4 \times 3 - 1 = 119 $

The curve is concave up in $ (-\infty, 3) $ and is concave down in $ (3, \infty) $.