Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(x)=(2x2+3x)g(x) for all x where g(x) is continuous and g(0)=9 then f'(0) is equals to
Options:
A .  
9
B .  
3
C .  
27
D .  
6
Answer: Option C : C f′(x)=limh→0f(x+h)−f(x)h =limh→0f(x)+f(h)−f(x)h =limh→0(2h2+3h)g(h)h =limh→0(2h+3)g(h) =3g(0) =27
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