What are the extreme points of a function?

In math, the extreme points of a function are the points at which the function reaches its highest or lowest values, and these points are called local maximum and minimum, respectively.

How do you find the extreme points of an function?

To find the extreme points of a function, differentiate the function to find the slope of the tangent lines at each point, set the derivative equal to zero, and solve for x to find the x-coordinates of the extreme points. Then, substitute the x-values back into the original function to find the y-coordinates of the extreme points.

How do you determine whether an extreme point is maximum or minimum?

To determine whether an extreme point is maximum or minimum, differentiate the function twice to find the second derivative and evaluate the second derivative at the extreme point. If the second derivative is positive, the extreme point is a minimum, and if it is negative, the extreme point is a maximum. If the second derivative is zero, the test is inconclusive and the use of additional methods is needed.

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

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(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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Frequently Asked Questions (FAQ)

What are the extreme points of a function?
In math, the extreme points of a function are the points at which the function reaches its highest or lowest values, and these points are called local maximum and minimum, respectively.
How do you find the extreme points of an function?
To find the extreme points of a function, differentiate the function to find the slope of the tangent lines at each point, set the derivative equal to zero, and solve for x to find the x-coordinates of the extreme points. Then, substitute the x-values back into the original function to find the y-coordinates of the extreme points.
How do you determine whether an extreme point is maximum or minimum?
To determine whether an extreme point is maximum or minimum, differentiate the function twice to find the second derivative and evaluate the second derivative at the extreme point. If the second derivative is positive, the extreme point is a minimum, and if it is negative, the extreme point is a maximum. If the second derivative is zero, the test is inconclusive and the use of additional methods is needed.

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

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