Question

Let f(x + y) = f(x) f(y) for all x and y. If f(5) = 2 and f′(0) = 3, then f′(5) is equal to:

• A. 5
• B. 6
• C. 0
• D. None of these

Answer 1

Answer: (B)

6

Answer 2

f′(5) = $\lim _ { h \rightarrow 0 }$ $\frac{f(5 + h) - f(5)}{h}$

= $\lim _ { h \rightarrow 0 }$ $\frac{f(5)f(5) - f(5)f(0)}{h}$

= f(5) $\lim _ { h \rightarrow 0 }$ $\frac{f(h) - f(0)}{h}$= f(5) f′(0) = 2.3 = 6