Differential Question

[kevinsachdev]

Suppose that g is a differentiable function and that f(x) = g(x) + 5 for all x. If g'(1) = 3 then f'(1) = ? explain your answer.

 

[Deleted member 4993]

Suppose that g is a differentiable function and that f(x) = g(x) + 5 for all x. If g'(1) = 3 then f'(1) = ? explain your answer.

From the given equation (f(x) = g(x) + 5), derive a relationship between f'(x) and g'(x).

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[HallsofIvy]

It is a very basic rule of Calculus that (f(x)+ g(x))'= f'(x)+ g'(x)! Surely that is in your textbook?

 

[JeffM]

It is possible that you don't yet know any general laws of derivatives. In which case you can use the definition of derivatives

[MATH]g(x) = f(x) + 5 \implies[/MATH]
[MATH]g'(x) = \lim_{h \rightarrow 0} \dfrac{\{f(x + h) + 5\} - \{f(x) + 5\}}{h} = \lim_{h \rightarrow 0} \dfrac{f(x + h) - f(x)}{h} = WHAT?[/MATH]