Please help me, find the answer

Question

Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation)

f(x) = x⁴ − 9x³

^{Concave Upward=}

Answer 1

f(x) = x^4 -9x^3

f'(x) = 4x^3 -27x^2

f"(x) = 12x^2 - 54x = 0

2x^2 -9x = 0

x(2x-9) =0

x =0, 9/2 or 0, 4.5

concave upward = (-infinity, 0) and (4.5, infinity)

concave downward = (0, 4.5)