critical points of y=(x^2+x+1)/x

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

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log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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critical points y=x²+x+1x

Solution

x=−1, x=1

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x²+x+1x

Critical point definition

Critical points are points where the function is defined and its derivative is zero or undefined

Find where f ′(x) is equal to zero or undefined

x=−1, x=1, x=0

Identify critical points not in f(x) domain

Domain of x²+x+1x : x<0 or x>0

x²+x+1x is not defined at x=0, therefore:

x=−1, x=1

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domain x²+x+1x

range x²+x+1x

inverse x²+x+1x

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

critical points of y=(x^2+x+1)/x

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