bobcat817
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Homework Statement
Let y be a fixed real number satisfying 0<y\leq1. Prove that (1+x)^{y}\leq1+ x^{y} for all x\geq0.
Homework Equations
I'm not sure.
The Attempt at a Solution
The hint given with the problem states that the derivative of x^{y} is yx^{y-1}. My first thought is that I'm supposed to show that they are both strictly increasing, but I don't really know what that would help me with.
I'm not really looking for an answer so much as a bit of direction.