Math 22 Increasing and Decreasing Functions - Revision history

Tphan046 at 15:29, 28 July 2020

2020-07-28T15:29:41Z

2020-07-28T15:26:56Z

Increasing and Decreasing Test

2020-07-28T15:25:17Z

Increasing and Decreasing Test

2020-07-28T15:21:26Z

Increasing and Decreasing Test

2020-07-28T15:11:43Z

Critical Numbers and Their Use

2020-07-28T15:10:49Z

Increasing and Decreasing Test

2020-07-28T15:10:32Z

2020-07-28T15:03:47Z

Critical Numbers and Their Use

2020-07-28T15:03:32Z

Critical Numbers and Their Use

2020-07-28T14:55:15Z

← Older revision		Revision as of 15:29, 28 July 2020
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−	==Definitions of Increasing and Decreasing Functions.	+	==Definitions of Increasing and Decreasing Functions==

	A function is increasing on an interval when, for any two numbers <math>x_1</math> and		A function is increasing on an interval when, for any two numbers <math>x_1</math> and

@@ Line 50: / Line 50: @@
    whether <math>f</math> is increasing or decreasing on each interval.
-'''Exercises:''' Find critical numbers of
+'''Exercises:''' Find the intervals of increasing and decreasing of
 '''1)''' <math>f(x)=x^3-3x^2</math>
@@ Line 69: / Line 69: @@
 |-
 |<math>f'(3)=9>0</math>, so <math>f(x)</math> is increasing on <math>(2,\infty)</math>
 |}

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 |-
 |Hence, the test intervals are <math>(-\infty,0),(0,2)</math> and <math>(2,\infty)</math>
 |}
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''

@@ Line 49: / Line 49: @@
 . Use the test for increasing and decreasing functions to decide
    whether <math>f</math> is increasing or decreasing on each interval.
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''

@@ Line 19: / Line 19: @@
    undefined.
-Exercises: Find critical numbers of
+'''Exercises:''' Find critical numbers of
 '''1)''' <math>f(x)=x^2+2x</math>

@@ Line 44: / Line 44: @@
 . Find the derivative of <math>f</math>.
-. Locate the critical numbers of <math>f</math> and use these numbers to determine test intervals. That is, find all <math>f</math> for which <math>f'(x)=0</math> or <math>f'(x)</math> is undefined.
+. Locate the critical numbers of <math>f</math> and use these numbers to determine test intervals.
 . Determine the sign of <math>f'(x)</math> at one test value in each of the intervals.
-. Use the test for increasing and decreasing functions to decide whether <math>f</math> is increasing or decreasing on each interval.
+. Use the test for increasing and decreasing functions to decide
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''

@@ Line 38: / Line 38: @@
 |So, <math>f'(x)=\frac{1}{2}x^{\frac{-1}{2}}=\frac{1}{2\sqrt{x}}</math>
 |-
-|In this case, we have critical number when <math>f'(x)</math> is undefined, which is when <math>sqrt{x}=0</math>. So critical number is <math>x=0</math>
+|In this case, we have critical number when <math>f'(x)</math> is undefined, which is when <math>\sqrt{x}=0</math>. So critical number is <math>x=0</math>
 |}

@@ Line 16: / Line 16: @@
 ==Critical Numbers and Their Use==
-   If <math>f</math> is defined at <math>c</math>, then <math>c</math> is a critical number of <math>f</math>
+   If <math>f</math> is defined at <math>c</math>, then <math>c</math> is a critical number of <math>f</math> when <math>f'(c)=0</math> or when <math>f'(c)</math> is
- when <math>f'(c)=0</math> or when <math>f'(c)</math> is undefined.
+  undefined.
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''