YO, does anyone know calculus? ?

Find the number c that satisfies the conclusion of the Mean Value Theorem.

f(x)=x/x+4

[1, 8]

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  • Anonymous
    1 decade ago
    Favorite Answer

    well since the mean value theorem basically says, that with a function f(x) there are numbers (a and b) such that th slope of the line between the two points it equal to another number c so that if u plug c into the f ' (x) function you get the same number as the previous slop you calculated.

    if the numbers are 1 and 8 then you find f(1) and f(8) then using the points find m (slope) of the line connecting the two points. then using that number, figure out with the number c is. m=f ' (x)

    i tried calculating this, however i think i may have made a math error since my m=1/15 and then that left me with a formula that i can not factor x2-22x-44=0. and i can't remember the quadratic formula...

  • 1 decade ago

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

    f'(x)=[(x+4) - x] / (x+4)^2 = 4 / (x+4)^2

    f'(c) = 4 / (c+4)^2 = [8/(8+4)] / (8-1) = (8/12) / 7 = 8/84 = 2/21

    [4/ (c+4)^2] = 2/21

    The value of c that satisfies this equation is 2.480740698.

  • 1 decade ago

    first compute f '(x) = (d/dx) f(x) = 4/(x+4)^2

    mean-value theorem says f(8) - f(1)= f '(c)*(8-1) for some c in [1,8].

    hence solve for c : (8/12) - (1/5) = [2/(c+4)]^2*7

    or, (1/15) = [2/(c+4)]^2

    or, c= 2*sqrt(15) - 4 = 3.746 approx.

  • 1 decade ago

    f(x)= √c-4/x^2

    f(x)=c-4

    c=f(x) -4 +1= f(x) -3

    and u can continue it from here..

    u know calculus is not easy ;)... it will take time to calculate like this things

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  • 1 decade ago

    Sorry but I'm really bad at math.

  • 1 decade ago

    6. Trust me.... 6. Every body who looks at this thing, give me a thumbs up!! I BEG OF YOU!!! PLEASSSSEEEE!

  • 1 decade ago

    yes i do know calculus!

  • 1 decade ago

    No man, not yet sorry.

  • Anonymous
    1 decade ago

    yo dawg, no.

  • 1 decade ago

    yo.

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