![f(x)= \sqrt{2} (x-1)+\cos2x
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f'(x)= \sqrt{2} -2\sin2x
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f'(x)=0
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\sqrt{2} -2\sin2x=0
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\sin2x= \frac{ \sqrt{2} }{2}
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2x=(-1)^k \frac{ \pi }{4} + \pi k
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x=(-1)^k \frac{ \pi }{8} + \frac{\pi k}{2} , \ k\in Z](https://tex.z-dn.net/?f=f%28x%29%3D+%5Csqrt%7B2%7D+%28x-1%29%2B%5Ccos2x%0A%5C%5C%5C%0Af%27%28x%29%3D+%5Csqrt%7B2%7D+-2%5Csin2x%0A%5C%5C%5C%0Af%27%28x%29%3D0%0A%5C%5C%5C%0A+%5Csqrt%7B2%7D+-2%5Csin2x%3D0%0A%5C%5C%5C%0A%5Csin2x%3D+%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B2%7D+%0A%5C%5C%5C%0A2x%3D%28-1%29%5Ek+%5Cfrac%7B+%5Cpi+%7D%7B4%7D+%2B+%5Cpi+k%0A%5C%5C%5C%0Ax%3D%28-1%29%5Ek+%5Cfrac%7B+%5Cpi+%7D%7B8%7D+%2B++%5Cfrac%7B%5Cpi+k%7D%7B2%7D+%2C+%5C+k%5Cin+Z "f(x)= \sqrt{2} (x-1)+\cos2x
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f'(x)= \sqrt{2} -2\sin2x
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f'(x)=0
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\sqrt{2} -2\sin2x=0
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\sin2x= \frac{ \sqrt{2} }{2}
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2x=(-1)^k \frac{ \pi }{4} + \pi k
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x=(-1)^k \frac{ \pi }{8} + \frac{\pi k}{2} , \ k\in Z")
0
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-\sin x+\frac{1}{2} >0
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-\sin x>-\frac{1}{2}
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\sin x<\frac{1}{2}
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x\in(- \frac{7 \pi }{6} +2 \pi n; \ \frac{ \pi }{6} +2 \pi n), \ n\in Z" alt="f(x)=\cos x+\frac{x}{2}
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f'(x)=-\sin x+\frac{1}{2}
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f'(x)>0
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-\sin x+\frac{1}{2} >0
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-\sin x>-\frac{1}{2}
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\sin x<\frac{1}{2}
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x\in(- \frac{7 \pi }{6} +2 \pi n; \ \frac{ \pi }{6} +2 \pi n), \ n\in Z" align="absmiddle" class="latex-formula">