Question

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

• A. 6
• B. 3
• C. 1
• D. None of these

Hint:

Use differentiation and known values to calculate the derivative at the desired point.

Answer 1

The Correct Option is A

Step 1: Differentiate the equation.
We differentiate both sides of \( f(x + y) = f(x) \cdot f(y) \) with respect to \( x \) and use the given values \( f(5) = 2 \) and \( f'(0) = 3 \) to find \( f'(5) = 6 \).
Thus, the correct answer is (1).