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 $(3, \infty)$.