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Math Help - Mean Value Theorem stuff

  1. #1
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    Mean Value Theorem stuff

    If anyone can help get me started on these two problems, I'd be greatful =)

    1. Verify that the function satisfies the hypothesis of the Mean Value Theorem on the given interval. Then find all the numbers c that satisfy the conclusion of the given interval

    f(x) = x/(x+2) on [1,4]

    2. If f'(x) is greater than or equal to M on [a,b], show that f(b) is greater than or equal to f(a) + M(b-a)

    I am having a hard time wrapping my head around these two, so if someone could help explain how to go about looking at problems of these sorts... that'd be nice

    Thanks guys!


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  2. #2
    Junior Member frenzy's Avatar
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    2)

    (f(b)-f(a))/(b-a)=f'(c)>=M

    so

    f(b)-f(a)>=M(b-a)

    f(b)>=f(a)+M(b-a)
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  3. #3
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    Can you explain that to me? Please =)
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  4. #4
    Junior Member frenzy's Avatar
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    The MVT says that

    (f(b)-f(a))/(b-a)=f'(c)

    for some c in (a,b)

    we are given f'(x)>=M for all x in [a,b]

    therefore f'(c)>=M


    so...


    (f(b)-f(a))/(b-a)=f'(c)>=M

    multiply both sides by (b-a)

    f(b)-f(a)>=M(b-a)

    add f(a) to both sides

    f(b)>=f(a)+M(b-a)
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  5. #5
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    Thanks bro!
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