Let f be a function such that $f(x + y) = f (x)+ f (y)$ for all x and y and $f (x) (2x^2+ 3x) g(x)$ for all x, where g(x) is continuous and g(0) = 3. Then f'(x) is equal to
Answer & explanation
Correct answer: option 1
$f'(x)=\underset{h→0}{\lim}\frac{f(x+h)-f(x)}{h}=\underset{h→0}{\lim}\frac{f(x)+f(h)-f(x)}{h}=\underset{h→0}{\lim}\frac{f(h)}{h}$
$=\underset{h→0}{\lim}\frac{(2h^2+3h)g(h)}{h}=3g(0)=9$