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If f''(x) =- f(x) and g(x) = f'(x) and F...

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

A

5

B

10

C

0

D

15

Text Solution

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To solve the problem, we need to analyze the given information step by step. ### Step 1: Understand the given equations We have: 1. \( f''(x) = -f(x) \) 2. \( g(x) = f'(x) \) This means that \( f(x) \) is a function whose second derivative is the negative of the function itself, which is characteristic of trigonometric functions like sine and cosine. ...
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