Doubt in definition of derivative $\lim_{s\to 0} \frac{f(2+s)-f(2)}{2s} = 1$

Question

I'm trying to solve a test and I have a doubt. Knowing the following limit

$$\lim_{s\to 0} \frac{f(2+s)-f(2)}{2s} = 1$$

can someone help me to choose the right option?

a) $f'(2) = 1 $

b) $f'(2) = 2 $

c) $f'(0) = 1 $

Answer 1

You know that $$\lim_{s\to0}\frac{f(2+s)-f(2)}s=2.$$ Hence, $f'(2)=2$.

Answer 2

Hint

$$\lim_{s\to 0}\frac{f(2+s)-f(2)}{s}=f'(2).$$

Answer 3

I would avoid asking test question on stack exchange. It only hinders your learning, but you get to choose how much you want to learn. What is shown in the question is the definition of the derivative multiplied by 1/2. i.e

$1/2 *f'(2)= 1$

Therefore, the answer is b.