Answer:
D: 0 and 1
Step-by-step explanation:
Function is defined by;
f(x) = 3x^(5) - 5x⁴
Now, an inflection point will be a point on the graph where the inflection or concavity changes.
Thus, let's find the derivatives until we get there;
f'(x) = 15x⁴ - 20x³
f''(x) = 60x³ - 60x²
So factorizing gives;
f''(x) = 60x²(x - 1)
At f''(x) = 0, we have; x = 0 or x = 1
Thus, the x coordinates of points of inflection are 0 & 1
