Difference between revisions of "009A Sample Final 1, Problem 7"

Latest revision as of 15:55, 2 December 2017

A curve is defined implicitly by the equation

x^{3}+y^{3}=6xy.

(a) Using implicit differentiation, compute ${\frac {dy}{dx}}$ .

(b) Find an equation of the tangent line to the curve $x^{3}+y^{3}=6xy$ at the point $(3,3)$ .

Solution

Detailed Solution

Return to Sample Exam

@@ Line 1: / Line 1: @@
-<span class="exam">A curve is defined implicityly by the equation
+<span class="exam">A curve is defined implicitly by the equation
-::::::<math>x^3+y^3=6xy</math>
+::<math>x^3+y^3=6xy.</math>
-<span class="exam">a) Using implicit differentiation, compute <math>\frac{dy}{dx}</math>.
+<span class="exam">(a) Using implicit differentiation, compute &nbsp;<math style="vertical-align: -12px">\frac{dy}{dx}</math>.
-<span class="exam">b) Find an equation of the tangent line to the curve <math>x^3+y^3=6xy</math> at the point <math>(3,3)</math>.
+<span class="exam">(b) Find an equation of the tangent line to the curve &nbsp;<math style="vertical-align: -4px">x^3+y^3=6xy</math>&nbsp; at the point &nbsp;<math style="vertical-align: -5px">(3,3)</math>.
+<hr>
+[[009A Sample Final 1, Problem 7 Solution|'''<u>Solution</u>''']]
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Foundations: &nbsp;
-|-
-|
-|}
-'''Solution:'''
+[[009A Sample Final 1, Problem 7 Detailed Solution|'''<u>Detailed Solution</u>''']]
-'''(a)'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
-|-
-|Using implicit differentiation on the equation <math>x^3+y^3=6xy</math>, we get
-|-
-|<math>3x^2+3y^2\frac{dy}{dx}=6y+6x\frac{dy}{dx}</math>.
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
-|-
-|Now, we move all the <math>\frac{dy}{dx}</math> terms to one side of the equation.
-|-
-|So, we have
-|-
-|<math>3x^2-6y=\frac{dy}{dx}(6x-3y^2)</math>.
-|-
-|We solve for <math>\frac{dy}{dx}=\frac{3x^2-6y}{6x-3y^2}</math>.
-|}
-'''(b)'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
-|-
-|
-|-
-|
-|-
-|
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
-|-
-|
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 3: &nbsp;
-|-
-|
-|-
-|
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Final Answer: &nbsp;
-|-
-|'''(a)'''
-|-
-|'''(b)'''
-|}
 [[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Difference between revisions of "009A Sample Final 1, Problem 7"

Latest revision as of 15:55, 2 December 2017

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