Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x^(1/3) + 6x^(4/3). You must justify your answer using an analysis of f '(x) and f "(x).

Question

I found the first and second derivative which i think is (8x+1)/(x^(2/3), and the second is 2(4x-1)/3x^(5/3). what now?

Answer 1

Assuming x is not zero, the fractions are zero when the numerators are zero.

So,

f'=0 when 8x+1 = 0, or x = -1/8
f"=0 when 4x-1 = 0, or x = 1/4