critical points of {sin(x):x<0,2x:x>= 0}

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

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critical points {sin(x):x<0, 2x:x≥ 0}

Solution

x=π2 +2πn, x=3π2 +2πn, x=0

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{sin(x):x<0, 2x:x≥ 0}

Critical point definition

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

Critical Points of {sin(x):x<0}: x=π2 +2πn, x=3π2 +2πn

Critical Points of {2x:x≥ 0}: None

Combine critical points of all pieces:

x=π2 +2πn, x=3π2 +2πn

Evaluate interval endpoint x=0: critical point

x=π2 +2πn, x=3π2 +2πn, x=0

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היי, לשאול שאלה לגבי critical points {sin(x):x<0,2x:x≥ 0} או בחר למטה

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

`x`²	`x`<−2
ln(`x`+5)	`x`≥−2

√`x`+2	`x`<1
`xx`²−6`x`+8	`x`≥1

√`x`²−4	`x`<0
`x`³−`x`	`x`≥0

critical points of {sin(x):x<0,2x:x>= 0}

Solution

Solution steps

Number Line

Graph

sin(`x`)	`x`<0
2`x`	`x`≥0