If `f''(x)=-f(x) and g(x)=f^(prime)(x)` and `F(x)=(f(x/2))^2+(g(x/2))^2` and given that `F(5)=5,` then `F(10)` is (a)5 (b) 10 (c) 0 (d) 15

Options

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

Explanation

To solve the problem, we start with the information given:

1. We have the second derivative of a function \( f \) given by the equation:
\[ f''(x) = -f(x) \]
2. We define \( g(x) = f'(x) \).
3. We also have the function \( F(x) \) defined as:
...