Question

If ∀x & y, f(x + y) = f(x)⋅f(y) and f(5) = 2, f ′(0) = 3

then f ′(5) equals

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (D)

6

Answer 2

f(x) = a^x

f(x) = a⁵ = 2

f′(x) = $a^{x}\log_{e}a$

f′(0) = $\log_{e}a = 3$

f′(5) = a⁵$\log_{e}a = 2.3 = 6$