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Find `g'(4)` given that `f(4)=5`  and `f'(4)=1` and `g(x)=f(x)/x`.   

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user7230927 | (Level 1) Salutatorian

Posted June 29, 2013 at 1:32 AM via web

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Find `g'(4)` given that `f(4)=5`  and `f'(4)=1` and `g(x)=f(x)/x`. 


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mjripalda | High School Teacher | (Level 1) Senior Educator

Posted June 29, 2013 at 1:51 AM (Answer #1)

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To solve for g'(4), take the derivative of g(x). To do so, apply quotient rule which is `(u/v)'=(v*u'-u*v')/v^2` .


Since the expression for the function f(x) is not given, then its derivative is expressed as f'(x) only.



Then, plug-in x=4 to get the value of g'(4).



Also, plug-in the given values of f(4) and f'(4) which are 5 and 1, respectively.





Hence, `g'(4)=-1/16` .

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