Calculus Question in Description

Question

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.

Answer 1

Given that f(x) = g(x) + 5, we can find the derivative of f:

f'(x)=g'(x) (the 5 is annihilated in the differentiation).

Therefore, f'(1)=g'(1)=3.

The 2 functions behave identically with the exception of the vertical shift of 5. That shift does not affect the slope of the function.