Question

If f is the function defined by f(x) = 3x^5 - 5x^4, what are all the x coordinates of points of inflection for the graph of f?

a. -1
b. 0
c. 1
d. 0 and 1
e. -1, 0, and 1

Answer 1

D: 0 and 1

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