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Math Help - Mean Value Theorem

  1. #1
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    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!!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    multiply both sides by sqrt(x)

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

    result follows
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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