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jazz1234567890
Group Title
Identify the relative maximum value for the function shown below.
7/x^2 + 5
 one year ago
 one year ago
jazz1234567890 Group Title
Identify the relative maximum value for the function shown below. 7/x^2 + 5
 one year ago
 one year ago

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richyw Group TitleBest ResponseYou've already chosen the best response.1
please typeset the function properly
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.1
Is this what you want (because this is what you typed) \[\frac{7}{x^2}+5\]
 one year ago

jazz1234567890 Group TitleBest ResponseYou've already chosen the best response.0
7 divided by x2+5
 one year ago

jazz1234567890 Group TitleBest ResponseYou've already chosen the best response.0
dw:1352146335340:dw
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.1
\[f(x)=\frac{7}{x^2+5}\]To maximize the function, take the derivative wrt x\[\frac{df}{dx}=\frac{d}{dx}\left(7(x^2+5)^{1}\right)\]\[\frac{df}{dx}=7\frac{d}{dx}(x^2+5)^{1}\]Use the chain rule...\[\frac{df}{dx}=7\left(1(x^2+5)^{2}\cdot \frac{d}{dx}(x^2+5)\right)\]\[\frac{df}{dx}=7\left(\frac{2x}{\sqrt{x^2+5}}\right)\]\[\frac{df}{dx}=\frac{14x}{\sqrt{x^2+5}}\]
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.1
where \(\frac{df}{dx}=0\) you have a critical point. So solve this for zero. It is easy to see that this occurs only where x=0. So that is your critical point. So find the value of \(f(x=0)\) Which is obviously \[f(0)=\frac{7}{5}\]Which is the maximum value of the function. Note that just because it is a critical point does not neccesarily mean that it is the maximum value, you must also check the behaviour at infinity (or the edges of a region if you are looking for the maximum value over a region). However in this problem it was given to you that there was a maximum, plus it is easy to see that \[\lim_{x\rightarrow \pm \infty} f(x)=0\] So you can be sure this is the maximum.
 one year ago
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