Find e local maximum and local minima, of the function `f(x)= sin x-co – InterviewSolution

1.	Find e local maximum and local minima, of the function `f(x)= sin x-cos x`,`0
Answer» 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)` `:. f(x)_(max) = sqrt2` `f(x)_(min) = -sqrt2`

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