I need help determining the intervals of increase, decrease and the intervals of upward and downward concavity given f prime.
f'(x)=(64x^4 - 125x) ^(-2/3).
Im not sure how to solve this. I know that the function has no intervals of decrease, its the rest im having trouble with
f is increasing where f' > 0
f' = 1/∛(x(64x^3-125))^2
Since (x(64x^3-125))^2 is always positive, f' is always positive, so f is always increasing.
f is concave up when f" > 0
f" = (250-512x^3)/(2(64x^4 - 125x) ^(5/3))
So, f"=0 at x = ∛(250/512)