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If f'(x)=k(cos x-sinx), f'(0)=3, f((pi)/...

If f'(x)=k(cos x-sinx), f'(0)=3, `f((pi)/(2))=15`, find f(x)

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Given, `f(x)=k(cosx-sinx)`
`f'(0)=3` (Given)
`thereforek(1-0)=3`
k=3
Now , `(d)/(dx)f(x)=3(cosx-sinx)`
`f(x)=int3(cosx-sinx)dx`
`=3(sinx+cosx)+c`
`f((pi)/(2))=15` (Given)
Now , `15=3("sin"(pi)/(2)+"cos"(pi)/(2))+c`
c =12
Then , `f(x)=3(sinx+cosx)+12`
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