Question

Let g : R ® R be a differentiable function satisfying

g(x) = g(y) g(x – y) " x, y Î R and g'(0) = a and g'(3) = b then g'(– 3) is –

• A. $\frac{a^{2}}{b}$
• B. $\frac{a}{b}$
• C. $\frac{b}{a}$
• D. None of these

Answer 1

Answer: (A)

$\frac{a^{2}}{b}$

Answer 2

Differentiating partially w.r.t. x

g'(x) = g(y)[g'(x – y)]

Put y = x

g'(x) = g(x) . g'(0) = a . g(x)

̃ g(x) = ae^x (Q g(0) = 1)

Now g'(x) = ae^x, g'(3) = ae³

and g' (–3) = ae^–3 = $\frac{a^{2}}{b}$