If , where is a continuous double differentiable function and . If and , then…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

f''(x) = -f(x)

, where

f(x)

is a continuous double differentiable function and

g(x) = f'(x)

. If

F(x) = \left\{ f\left(\frac{x}{2}\right) \right\}^2 + \left\{ g\left(\frac{x}{2}\right) \right\}^2

and

F(5) = 5

, then

F(10)

is (1) 0 (2) 5 (3) 10 (4) 25