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Find e local maximum and local minima, o...

Find e local maximum and local minima, of the function `f(x)= sin x-cos x`,`0

Text Solution

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Here, `f(x) = sinx-cosx`
`f(x) = sqrt2(1/sqrt2sinx-1/sqrt2cosx)`
`= sqrt2(cos(pi/4) sinx-sin(pi/4) cosx)`
`=sqrt2(sin(x-pi/4))`
So, `f(x)` will be maximum when `sin(x-pi/4) = 1`
`=> sin(x-pi/4) = sinpi/2=> x-pi/4 = pi/2=>x = (3pi/4)`
`f(x)` will be minimum when `sin(x-pi/4) = -1`
`=> sin(x-pi/4) = sin-pi/2=> x-pi/4 = -pi/2=>x = (-pi/4)`
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