009A Sample Final 3, Problem 9 - Revision history

Kayla Murray at 23:47, 2 December 2017

2017-12-02T23:47:28Z

2017-03-07T19:18:00Z

2017-03-07T19:12:26Z

2017-03-07T18:58:24Z

2017-03-06T21:39:11Z

2017-03-06T21:38:25Z

2017-02-19T02:03:49Z

2017-02-18T02:35:31Z

@@ Line 7: / Line 7: @@
 <span class="exam">(b) Find absolute maximum and absolute minimum of &nbsp;<math style="vertical-align: -4px">g</math>&nbsp; over &nbsp;<math style="vertical-align: -5px">[0,8].</math>
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009A Sample Final 3, Problem 9 Solution|'''<u>Solution</u>''']]
-'''Solution:'''
+[[009A Sample Final 3, Problem 9 Detailed Solution|'''<u>Detailed Solution</u>''']]
 [[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 56: / Line 56: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Step 2: &nbsp;
 |-
+|
@@ Line 95: / Line 67: @@
 |-
 |'''(b)'''
 |}
 [[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 3: / Line 3: @@
 ::<math>g(x)=(2x^2-8x)^{\frac{2}{3}}</math>
-<span class="exam">(a) Find all critical points of <math>g</math> over the <math>x</math>-interval <math>[0,8].</math>
+<span class="exam">(a) Find all critical points of &nbsp;<math style="vertical-align: -4px">g</math>&nbsp; over the &nbsp;<math style="vertical-align: 0px">x</math>-interval &nbsp;<math style="vertical-align: -5px">[0,8].</math>
-<span class="exam">(b) Find absolute maximum and absolute minimum of <math>g</math> over <math>[0,8].</math>
+<span class="exam">(b) Find absolute maximum and absolute minimum of &nbsp;<math style="vertical-align: -4px">g</math>&nbsp; over &nbsp;<math style="vertical-align: -5px">[0,8].</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"

@@ Line 1: / Line 1: @@
 <span class="exam">Let
-::::<math>g(x)=(2x^2-8x)^{\frac{2}{3}}</math>
+::<math>g(x)=(2x^2-8x)^{\frac{2}{3}}</math>
-::<span class="exam">a) Find all critical points of <math>g</math> over the <math>x</math>-interval <math>[0,8].</math>
+<span class="exam">(a) Find all critical points of <math>g</math> over the <math>x</math>-interval <math>[0,8].</math>
-::<span class="exam">b) Find absolute maximum and absolute minimum of <math>g</math> over <math>[0,8].</math>
+<span class="exam">(b) Find absolute maximum and absolute minimum of <math>g</math> over <math>[0,8].</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 18: / Line 18: @@
+|
 |}
 '''Solution:'''
@@ Line 86: / Line 87: @@
+|
 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam">Let
-::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
+::::<math>g(x)=(2x^2-8x)^{\frac{2}{3}}</math>
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
+::<span class="exam">a) Find all critical points of <math>g</math> over the <math>x</math>-interval <math>[0,8].</math>
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
+::<span class="exam">b) Find absolute maximum and absolute minimum of <math>g</math> over <math>[0,8].</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"

@@ Line 77: / Line 77: @@
 !Step 1: &nbsp;
 |-
+|We need to compare the values of &nbsp;<math style="vertical-align: -5px">g(x)</math>&nbsp; at the critical points and at the endpoints of the interval.
 |-
+|Using the equation given, we have &nbsp;<math style="vertical-align: -5px">g(0)=0</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">g(8)=16.</math>
 |}
@@ Line 85: / Line 85: @@
 !Step 2: &nbsp;
 |-
+|Comparing the values in Step 1 with the critical points in (a), the absolute maximum value for &nbsp;<math style="vertical-align: -5px">g(x)</math>&nbsp; is &nbsp;<math style="vertical-align: -1px">16</math>
 |}
@@ Line 92: / Line 94: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp; &nbsp;'''(a)'''&nbsp; &nbsp;&nbsp;<math>(0,0),(2,4),(4,0).</math>
+|&nbsp; &nbsp;'''(a)'''&nbsp; &nbsp;<math>(0,0),(2,4),(4,0).</math>
 |-
-|'''(b)'''
+|&nbsp; &nbsp;'''(b)'''&nbsp; &nbsp;The absolute maximum value for &nbsp;<math style="vertical-align: -5px">g(x)</math>&nbsp; is &nbsp;<math style="vertical-align: -1px">16</math>&nbsp; and the absolute minimum value for &nbsp;<math style="vertical-align: -5px">g(x)</math>&nbsp; is &nbsp;<math style="vertical-align: -1px">0.</math>
 |}
 [[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 10: / Line 10: @@
 !Foundations: &nbsp;
 |-
+|'''1.''' To find the critical points for &nbsp;<math style="vertical-align: -5px">f(x),</math>&nbsp; we set &nbsp;<math style="vertical-align: -5px">f'(x)=0</math>&nbsp; and solve for &nbsp;<math style="vertical-align: -1px">x.</math>
 |-
+|
 |-
+|'''2.''' To find the absolute maximum and minimum of &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; on an interval &nbsp;<math>[a,b],</math>
 |-
+|
 |}