The point of inflection is calculated by equating the second derivative to zero and determining x from there.
f"(x) = -x²2xsinx² + cosx²(2x) = 0
2xcosx² - 2x³sinx² = 0
2x (cosx² - xsinx²) = 0
2x = 0 ⇒ x = 0
cosx² - xsinx² = 0 ⇒ x = 3.82 (if you use shift+solve in your scientific calculator)
Thus, the function only has 1 point of inflection and it is at x = 0.
Since a cube is l x w x h, find the length of one side first:
∛8,000 = 20
The length of one side is 20 feet. This can represented as "s".
To find the area of one of the faces, use s²:
20² or 20 x 20 = 400
The area of one face is 400 ft²!