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Letf'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =f(sinx)+f(cosx) which of the following is true? |
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Answer» g(x) is DECREASING in `((pi)/(4),(pi)/(2))` or `g(x)=f(sinx)sinx+COS^(2)xf(sinx)` `f(cos x)sin^(2)x-f(cosxgt0forall x in (0,pi//2)` [as it is given `f(sinx)=f(cos x (pi//2-x))lt0` Thus g(x) is increasing in `(0,pi//2)`. Also` g(pi//4)=0` or `g(x)gt0forallx in ((pi)/(4),(pi)/(2))` and `g(x) ltforall x in (0,pi//4)` Thus g(X) is decreasing in `(0,pi//4)` |
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