find-minimum-amp-maximum-value-of-function-f-x-sin-2-x-sin-x-1-2-pi-x-pi-

Question Number 85146 by john santu last updated on 19/Mar/20

find minimum & maximum value

of function

f (x) = - \sin^{2} x + \sin x - \frac{1}{2}, - π ⩽ x ⩽ π

Commented by mr W last updated on 19/Mar/20

f (x) = - (\sin^{2} x - \sin x + \frac{1}{4}) - \frac{1}{4}

= - {(\sin x - \frac{1}{2})}^{2} - \frac{1}{4}

f_{m a x} = - \frac{1}{4} a t \sin x = \frac{1}{2}, i . e . x = \frac{π}{6}, \frac{5 π}{6}

f_{m i n} = - \frac{5}{2} a t \sin x = - 1, i . e . x = - \frac{π}{2}

Answered by jagoll last updated on 19/Mar/20

Answered by Rio Michael last updated on 19/Mar/20

Maximum value = - 0.25

note at maximum vaue f^{^{'}} (x) = 0

minimum value = - 2.5