If f''(x) =- f(x) and g(x) = f'(x) and `F(x)=(f((x)/(2)))^(2)+(g((x)/(2)))^(2)`
and given that F(5) =5, then F(10) is

Options

A. 5
B. 10
C. 0
D. 15

Explanation

To solve the problem step by step, we will follow the reasoning laid out in the video transcript while providing a clearer structure and explanation.

### Given:
1. \( f''(x) = -f(x) \)
2. \( g(x) = f'(x) \)
3. \( F(x) = \left( f\left(\frac{x}{2}\right) \right)^2 + \left( g\left(\frac{x}{2}\right) \right)^2 \)
4. \( F(5) = 5 \)

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