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

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user7230927 | Salutatorian

Posted June 28, 2013 at 4:18 PM via web

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

express answers as reduced improper fractions 

`g'(4) = ??`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 28, 2013 at 4:32 PM (Answer #1)

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You need to evaluate derivative of the given function `g(x)` , such that:

`g'(x) = ((f(x))/4)' => g'(x) = (f'(x))/4`

You need to evaluate derivative of the function `g(x)` at `x = 4` , such that:

`g'(4) = (f'(4))/4`

Since the problem provides the information that `f'(4) = 1` , you need to replace 1 for `f'(4)` , such that:

`g'(4) = 1/4`

Since the numerator is smaller than denominator `(1 < 4)` , the derivative of the function `g(x)` at `x = 4` can only be expressed as a proper fraction.

Hence, evaluating g'(4), under the given conditions, yields that `g'(4)` is a proper fraction, `g'(4) = 1/4.`

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