Can the Mean Value Theorem Prove This Inequality for Positive Real Numbers?

[jspectral]

Homework Statement

Use the mean value theorem to show that if x ∈ ℝ>0 then 0 < ( x + 1)^1/5 − x^1/5 < (5x^4/5)^-1

Homework Equations

MVT: f(b) = f(a) + f ' (c)*(b-a)

The Attempt at a Solution

I can see that (5x^(4/5))^-1 is the differential of x^1/5, but I'm not sure what to let be f(x), what to let be a, and what to let be b. Thanks.

 

[HallsofIvy]

Try f(x)= x^{1/5} and apply the mean value theorem to the interval [x, x+ 1] (for fixed x).