A community for students.
Here's the question you clicked on:
 0 viewing
jazz1234567890
 3 years ago
Identify the relative maximum value for the function shown below.
7/x^2 + 5
jazz1234567890
 3 years ago
Identify the relative maximum value for the function shown below. 7/x^2 + 5

This Question is Closed

richyw
 3 years ago
Best ResponseYou've already chosen the best response.1please typeset the function properly

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

jazz1234567890
 3 years ago
Best ResponseYou've already chosen the best response.07 divided by x2+5

jazz1234567890
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1352146335340:dw

richyw
 3 years ago
Best 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...\[\frac{df}{dx}=7\left(1(x^2+5)^{2}\cdot \frac{d}{dx}(x^2+5)\right)\]\[\frac{df}{dx}=7\left(\frac{2x}{\sqrt{x^2+5}}\right)\]\[\frac{df}{dx}=\frac{14x}{\sqrt{x^2+5}}\]

richyw
 3 years ago
Best ResponseYou've already chosen the best response.1where \(\frac{df}{dx}=0\) 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.