How to prove an inequality (using convexity)

54 Views Asked by At

Say $a,b >0 $ and an integer $p >1$

Prove that $(a+b)^p < 2^{p-1}(a^p+b^p)$

I don't even know how to start, this exercise is on a convexity, concavity and Taylor practice, so my guess is that it is done with convexity.