Difference between revisions of "009A Sample Final 1, Problem 10"

Latest revision as of 16:17, 2 December 2017

If a resistor of $R$ ohms is connected across a battery of $E$ volts with internal resistance $r$ ohms, then the power (in watts) in the external resistor is

P={\frac {E^{2}R}{(R+r)^{2}}}.

If $E$ and $r$ are fixed but $R$ varies, what is the maximum value of the power?

Solution

Detailed Solution

Return to Sample Exam

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-<span class="exam">Consider the following continuous function:
+<span class="exam">If a resistor of &nbsp;<math style="vertical-align: 0px">R</math>&nbsp; ohms is connected across a battery of &nbsp;<math style="vertical-align: 0px">E</math>&nbsp; volts with internal resistance &nbsp;<math style="vertical-align: 0px">r</math>&nbsp; ohms, then the power (in watts) in the external resistor is
-::::::<math>f(x)=x^{1/3}(x-8)</math>
-<span class="exam">defined on the closed, bounded interval <math>[-8,8]</math>.
+::<math>P=\frac{E^2R}{(R+r)^2}.</math>
-<span class="exam">a) Find all the critical points for <math>f(x)</math>.
+<span class="exam">If &nbsp;<math style="vertical-align: 0px">E</math>&nbsp; and &nbsp;<math style="vertical-align: 0px">r</math>&nbsp; are fixed but &nbsp;<math style="vertical-align: 0px">R</math>&nbsp; varies, what is the maximum value of the power?
-<span class="exam">b) Determine the absolute maximum and absolute minimum values for <math>f(x)</math> on the interval <math>[-8,8]</math>.
+<hr>
+[[009A Sample Final 1, Problem 10 Solution|'''<u>Solution</u>''']]
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+[[009A Sample Final 1, Problem 10 Detailed Solution|'''<u>Detailed Solution</u>''']]
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 [[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Difference between revisions of "009A Sample Final 1, Problem 10"

Latest revision as of 16:17, 2 December 2017

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