CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Find the local maxima and local minima of the function $$f(x)=sin x-cos x, 0<x<2\pi$$. Also find the local maximum and local minimum values.


Solution

Given $$f(x)=\sin x-\cos x$$

differentiate on both sides

$$f^{ ' }\left( x \right) =\sin { x } +\cos { x } $$

$$ f^{ ' }\left( x \right) =0\Rightarrow x=\dfrac { 3\pi  }{ 4 } ,\dfrac { 7\pi  }{ 4 } $$

local maxima:
$$f^{ '' }\left( x \right) =\cos { x } -\sin { x } $$

$$ f^{ '' }\left( \dfrac { 3\pi  }{ 4 }  \right) =-\sqrt { 2 } <0,$$

$$ f\left( \dfrac { 3\pi  }{ 4 }  \right) =\sqrt { 2 } $$

local minima:
$$f^{ '' }\left( \dfrac { 7\pi  }{ 4 }  \right) =\sqrt { 2 } >0,\quad f\left( \dfrac { 3\pi  }{ 4 }  \right) =-\sqrt { 2 } $$

$$\sqrt { 2 }$$ and $$-\sqrt { 2 }$$ are the maximum and minimum values.  

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image