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

Expert Answers
lemjay eNotes educator| Certified Educator


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` .