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inflection points of f(x)=x^4-x^2

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

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ddx

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

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inflection points f(x)=x⁴−x²

Solution

(−1√6 , −536 ), (1√6 , −536 )

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Inflection points definition

An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.
If f ′′(x)>0 then f(x) concave upwards.
If f ′′(x)<0 then f(x) concave downwards.

f ′′(x)=12x²−2

Find intervals: Concave Upward:−∞ <x<−√16 , Concave Downward:−√16 <x<√16 , Concave Upward:√16 <x<∞

Plug x=−1√6 into x⁴−x²: −536

(−1√6 , −536 )

Plug x=1√6 into x⁴−x²: −536

(1√6 , −536 )

(−1√6 , −536 ), (1√6 , −536 )

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domain x⁴−x²

range x⁴−x²

inverse x⁴−x²

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

inflection points of f(x)=x^4-x^2

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