Let, then $$f(x)=xcos-1(-$$$$sin$$|x|$$)$$,x∈$$-$$π$$2$$,π$$2$$ which of the following is true?

Correct option is 4f' is decreasing in -π2,0 and increasing in 0,π2

Questions

$Let, then f (x) = {xcos}^{- 1} (- \sin | x |), x \in [- \frac{π}{2}, \frac{π}{2}] which of the following is true?$

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f'(0)=-π2

f is not differentiable at x=0

f' is increasing in -π2,0 and decreasing in 0,π2

f' is decreasing in -π2,0 and increasing in 0,π2

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detailed solution

Correct option is D

f(x)=xπ-cos-1(sin|x|)=xπ-π2-sin-1(sin|x|)=xπ2+|x|f(x)=xπ2+xx≥0xπ2-xx<0⇒f'(x)=π2+2xx≥0π2-2xx<0f'(x) is increasing in 0,π2 and decreasing in -π2,0

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Let, then f(x)=xcos-1(-sin|x|),x∈-π2,π2 which of the following is true?

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$Let, then f (x) = {xcos}^{- 1} (- \sin | x |), x \in [- \frac{π}{2}, \frac{π}{2}] which of the following is true?$