Question

If f (x + y) = f(x). f( y) ∀ x.y and f (5) = 2, f'(0) = 3 , then f'(5) is
(a) 0
(b) 1
(c) 6
(d) 2

Answer 1

Answer:

(c) 6

Step-by-step explanation:

use x, y=1

f(2) = f(1)^2

f(3) = f(1) f(2) = f(1)^3

f(4) = f(1) f(3) = f(1)^4

Therefore f(nx) = f(x)^n

nf'(nx) = nf(x)^n-1 f'(x)

f'(nx) = f(x)^n-1 f'(x)

putting n=0 we get

f'(0) = f'(x)/f(x)

putting x = 5

3 = f'(5)/2 . Hence f'(5) = 6