1)∣sec(x)∣<2tan(x) on[0,2π] 2)find the cirtical points and the range of f(x)=∣x−3∣+∣2x+1∣


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Question Number 84627 by M±th+et£s last updated on 14/Mar/20

$1) ∣ s e c (x) ∣< 2 t a n (x) o n [0, 2 π]$ $2) f i n d t h e c i r t i c a l p o i n t s a n d t h e r a n g e o f$ $f (x) =∣ x - 3 ∣ + ∣ 2 x + 1 ∣$
Commented byTANMAY PANACEA last updated on 14/Mar/20

$w h a t i s w u e s t i o n n o 1$
Commented byM±th+et£s last updated on 14/Mar/20

$s o l v e t h e i n e q u a l i t y$
	Answered by TANMAY PANACEA last updated on 14/Mar/20

	$2) f (x) =∣ x - 3 ∣ + ∣ 2 x + 1 ∣$ $c r i t i c a l v a l u e o f x a r e 3, - 0.5$ $f (x) = x - 3 + 2 x + 1$ $= 3 x - 2 w h e n x > 3$ $= 7 w h e n x = 3$ $= - (x - 3) - (2 x + 1) x < - 0.5$ $= - 3 x + 2$ $= 3.5 w h e n x = - 0.5$ $= - (x - 3) + 2 x + 1 w h e n 3 > x > - 0.5$ $= x + 4$ $s o f (x) \in [3.5, \infty)$
	Commented byjagoll last updated on 14/Mar/20

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