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Find all the points of local maxima and...

Find all the points of local maxima and minima of the function f given by `f(x)= sinx- cosx , x in [0,2pi]`

Text Solution

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`f(x)=sinx - cos x `
`f'(x)= cos x + sinx `
`=sqrt(2)sin(x+(pi)/(4))`
`f'(x)=0 at x=(3pi)/(4),(7pi)/(4)`

`(3pi)/(4)` is a point of local maxima .
`(7pi)/(4)` is a point of local minima.
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