QJEEM02Mae0b3: JEE Main 2002 Mathematics - Class 12 JEEM02Mae0b3 Solution: If f(x + y) = f(x).f(y) ∀ x, y and f(5) = 2, f'(0) = 3, then…

Question

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If f(x + y) = f(x).f(y)

\forall

x, y and f(5) = 2, f'(0) = 3, then
f'(5) is

Accepted Answer

f (x + y) = f (x) \times f (y)

Differeniate with respect to

x,

treating

y

as constant

f^{'} (x + y) = f^{'} (x) f (y)

Putting

x = 0

and

y = x

, we get

f^{'} (x) = f^{'} (0) f (x);

\Rightarrow f^{'} (5) = 3 f (5) = 3 \times 2 = 6.

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