Math miscellaneousEasy
Question
If f(x + y) = f(x) . f(y) ∀ x.y and f(5) = 2, f′(0) = 3 then f′(5)is
Options
A.0
B.1
C.6
D.2
Solution
f(x + y) = f(x) × f(y)
Differentiate 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); ⇒ f′(5) = 3f(5) = 3 × 2 = 6
Differentiate 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); ⇒ f′(5) = 3f(5) = 3 × 2 = 6
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