Calculus Help

posted by Mello

Use f(x)= 1/(square root(x)+1) to answer the following;
-- Use the difference quotient f'(x)=lim z->x (f(x)-f(z))/ (x-z) to find f'(x)!

Please show steps!!!

Thank you!!!

  1. Damon

    f(x) = 1/[ x^.5 +1 ]
    f(z) = 1/[ z^.5 + 1 }

    f(x)-f(z) = 1/[ x^.5 +1 ] - 1/[ z^.5 + 1]

    = ([z^.5+1]-[x^.5+1])/(x^.5z^.5 +x^.5+z^.5+1)

    = (z^.5-x^.5) /(x^.5z^.5 +x^.5+z^.5+1)
    Divide by (x-z) which is (x^.5-z^.5)(x^.5+z^.5)
    and get
    -(x^.5+z^.5) / (x^.5z^.5 +x^.5+z^.5+1)
    let z --->x
    - 2 x^.5 / (x +2 sqrt x + 1)
    check my arithmetic !!!

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