Answer:
{-3, 0, 6}
Step-by-step explanation:
There are points of inflection where the second derivative of f(x) is 0. That derivative is a cubic expression, so its zeros are most easily found using a graphing calculator. The attached shows its zeros to be at x = {-3, 0, 6}.
The x-values of the points of inflection are {-3, 0, 6}.
_____
The first derivative is ...
f'(x) = x^4 -4x^3 -36x^2
The second derivative is ...
f''(x) = 4x^3 -12x^2 -72x = 4x(x^2 -3x -18) = (4x)(x -6)(x +3)
It has zeros at x = -3, 0, +6.
