CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$f''(x)=-f(x)$$ and $$g(x)=f'(x)$$ and $$\displaystyle{F}({x})=\left ({f}\left (\frac{{x}}{2}\right)\right)^{2}+\left ({g}\left (\frac{{x}}{2}\right)\right)^{2}$$ and given that $$F(5)=5$$, then $$F(10)$$ is equal to 


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

Solution

The correct option is A $$5$$
$$\mathrm{f}''(\mathrm{x})=-\mathrm{f}(\mathrm{x})$$ and $$\mathrm{f'}(\mathrm{x})=\mathrm{g}(\mathrm{x})$$
$$\Rightarrow \mathrm{f}''(\mathrm{x}).\ \mathrm{f'}(\mathrm{x})+\mathrm{f}(\mathrm{x}).\ \mathrm{f'}(\mathrm{x})=0$$
$$Integrating,$$
$$(\mathrm{f'}(\mathrm{x}))^{2}+(\mathrm{f}(\mathrm{x}))^{2}=\mathrm{c}\Rightarrow(\mathrm{f}(\mathrm{x})^{2}+(\mathrm{g}(\mathrm{x}))^{2}=\mathrm{c}$$
$$\Rightarrow \mathrm{F}(\mathrm{x})=\mathrm{c}$$
$$\Rightarrow \mathrm{F}(10)=5$$ 

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image