1.

Find the points of localmaximaor minima for f(x) =" sin "2x -x, x in (0,pi)

Answer»

Solution :`f(X) =" sin "2x -x`
`f'(x) =2 COS 2x -1`
`f'(x) =0 ""rArr ""cos 2x=(1)/(2) ""rArr ""x=(pi)/(6),(5pi)/(6)`
`f''(x) =-4 sin 2x`
`f''((pi)/6) LT0 ""rArr "" "Maxima at " x=(pi)/(6)`
`f''((5pi)/(6)) gt 0 ""rArr """MINIMA at " x=((5pi)/(6))`


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