Find-minimum-and-maximum-of-f-x-9x-2-sin-2-x-4-x-sin-x-where-0-lt-x-lt-pi-

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 by bemath last updated on 04/Dec/20

s i r i g o t m a x = 18

Commented by bemath last updated on 04/Dec/20

s o r r y s i r . i w r o n g .

Commented by mr 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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