# Math Help - Mean Value Theorem

1. ## Mean Value Theorem

a. Use the Mean Value Theorem to show that for 0<x<y,

√y - √x < (y-x)/2√x.

b. Use part (a), above, to conclude that for 0<x<y,

√xy < (y+x)/2

I solved part (a), but I don't know how to solve part (b). Can somebody help please? Thanks!!

2. multiply both sides by sqrt(x)

then sqrt(xy) < (y-x)/2 + x

result follows