Let f(x+y)=f(x) · f(y) for all x, y where f(0) ≠ 0 If f(5)=2 and f^′(0)=3, then f^′(5) is equal to

Question

Let f(x+y)=f(x) · f(y) for all x, y where f(0) ≠ 0 If f(5)=2 and f^′(0)=3, then f^′(5) is equal to-

MARKS Content Team · Accepted Answer

Correct answer: (A) 6. f^′(5)=lim _h arrow 0 (f(5+h)-f(5))/h =lim _h arrow 0 (f(5+h)-f(5+0))/h =lim _h arrow 0 (f(5) · f(h)-f(5)+f(0))/h (∵ f(x+y)=f(x), f(y) for all x, y) = (lim _h arrow 0 (f(h)-f(0))/h ) · f(5)=f^′(0) · f(5) =3 × 2=6

Let $f(x+y)=f(x) \cdot f(y)$ for all $x, y$ where $f(0) \neq 0$ If $f(5)=2$ and $f^{\prime}(0)=3,$ then $f^{\prime}(5)$ is equal to-

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