Possible or not?

Calculus Level 3

Given that $f(x+y)=f(x)f(y)$ for all $x,y \in \mathbb R$ , $f(x) \ne 0$ , $f'(0)=2$ , and $f(2)=3$ .

Find $f'(2)$ .

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1 solution

Michael Huang
Dec 2, 2016

Let $x$ denote the variable of $f$ and $y = 2$ . Then, $f(x + 2) = f(x)f(2) = 3f(x)$ By chain rule , $f'(x + 2) = 3f'(x)$ Thus, if $x = 0$ $f'(2) = 3f'(0) = \boxed{6}$

Possible or not?

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