integral from 0 to 2pi of integral from 0 to 1 of integral from 4 to 4r^2 of cos(theta)r^2heta

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

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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 x⁴−x³

Solution

(0, 0), (12 , −116 )

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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)=12x²−6x

Find intervals: Concave Upward:−∞ <x<0, Concave Downward:0<x<12 , Concave Upward:12 <x<∞

Plug x=0 into x⁴−x³: 0

(0, 0)

Plug x=12 into x⁴−x³: −116

(12 , −116 )

(0, 0), (12 , −116 )

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domain x⁴−x³

range x⁴−x³

intercepts x⁴−x³

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

integral from 0 to 2pi of integral from 0 to 1 of integral from 4 to 4r^2 of cos(theta)r^2heta

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