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!!

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- August 14th 2009, 08:20 AMsun1Mean 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!! - August 14th 2009, 08:26 AMCalculus26
multiply both sides by sqrt(x)

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

result follows - August 14th 2009, 09:09 AMKrizalid