range of x^4-x^3

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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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Steps Examples

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range x⁴−x³

Solution

f(x)≥ −27256

Interval Notation

[−27256 , ∞ )

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Solution steps

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Function range definition

The set of values of the dependent variable for which a function is defined

Find the minimum and maximum value in each defined interval and unite the results

Domain of x⁴−x³ : −∞ <x<∞

Extreme Points of x⁴−x³: Saddle(0, 0), Minimum(34 , −27256 )

Find the range for the interval −∞ <x<∞ : −27256 ≤ f(x)<∞

Combine the ranges of all domain intervals to obtain the function range

f(x)≥ −27256

Solve instead

domain x⁴−x³

intercepts x⁴−x³

parity x⁴−x³

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