Find minimum and maximum of f(x)= ((9x^2 sin^2 x+4)/(x sin x)) where 0


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Question Number 124557 by bemath last updated on 04/Dec/20

$F i n d m i n i m u m a n d m a x i m u m$ $o f f (x) = \frac{9 x^{2} \sin^{2} x + 4}{x \sin x}$ $w h e r e 0 < x < π$
	Answered by mr W last updated on 04/Dec/20

	$n o m a x i m u m, s i n c e$ $\lim_{x \to 0, π} f (x) = + \infty$ $t = x \sin x > 0$ $f (x) = 9 t + \frac{4}{t} ⩾ {(3 \sqrt{t} - \frac{2}{\sqrt{t}})}^{2} + 12 ⩾ 12$ $\Rightarrow m i n i m u m = 12$
	Commented bybemath last updated on 04/Dec/20

	$s i r i g o t m a x = 18$
	Commented bybemath last updated on 04/Dec/20

	$s o r r y s i r . i w r o n g .$
	Commented bymr W last updated on 04/Dec/20

	$t h e r e i s o n l y l o c a l m a x i m u m, n o$ $g l o b a l m a x i m u m!$
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