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h(x), for which h(2)=2 and h'(2)=-1. Find f'(2) for the function f(x)=h(x)/x. when...

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jjmgingrich | Student, Undergraduate | Salutatorian

Posted February 22, 2013 at 7:10 PM via web

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h(x), for which h(2)=2 and h'(2)=-1. Find f'(2) for the function f(x)=h(x)/x. when f'(2)=???

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 22, 2013 at 7:16 PM (Answer #1)

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The function `f(x) = (h(x))/x` .

Using the quotient rule, `f'(x) = (h'(x)*x - h(x)*x')/(x^2)`

`f'(2) = (h'(2)*2 - h(2))/(2^2)`

= `(-1*2 - 2)/(2^2)`

= `-4/4`

= -1

The value of `f'(2) = -1`

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