Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
mickey
Group Title
f(x)=1/(4+9x^2)  sketch the region bounded by f, the xaxis, and the line x=1 and x=2
 3 years ago
 3 years ago
mickey Group Title
f(x)=1/(4+9x^2)  sketch the region bounded by f, the xaxis, and the line x=1 and x=2
 3 years ago
 3 years ago

This Question is Closed

julie Group TitleBest ResponseYou've already chosen the best response.0
hmmm, well, I think basically this is a second derivative function. Paul has some pretty good notes here on how to use the second derivative to glean more about the shape of a function http://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtII.aspx
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
Right now I'm watching this video: http://www.brightstorm.com/math/calculus/applicationsofthederivative/curvesketchingwithderivatives
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
seems to explain it well also. but yeah you need information from both the first and second derivatives in order to correctly sketch the region
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
been years since I've done so :p
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
$$f(x)=1/(4+9x ^{2})$$
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
^^ function using the equation editor thingy
 3 years ago

mickey Group TitleBest ResponseYou've already chosen the best response.0
Thanks Julie I think that helps me some!
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
hmmm, honestly going to have to look up the chain rule again lol
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
to even get the first derivative
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
hmmm. does anyone remember the chain rule? (looking)
 3 years ago

shadowfiend Group TitleBest ResponseYou've already chosen the best response.0
So we have: $$\frac{1}{4 + 9x^2}$$ Which makes: $$(4 + 9x^2)^{1}$$ We can apply the chain rule to this by first setting: $$ u = (4 + 9x^2) $$ And: $$\frac{d}{du} u^{1} = u^{2}$$
 3 years ago

shadowfiend Group TitleBest ResponseYou've already chosen the best response.0
But the chain rule says that taking the derivative of u when u consists of a function of x means we have to multiply by the derivative of the inner function: $$ \frac{d}{dx} \left(4 + 9x^2\right) = \frac{d}{dx}4 + \frac{d}{dx}9x^2 $$ We can apply basic power rule and such and get: $$ \frac{d}{dx} \left(4 + 9x^2\right) = 0 + 18x = 18x $$ And our end result is: $$ \left(4 + 9x^2\right)^2 \cdot 18x = \frac{18x}{\left(4 + 9x^2\right)^2} $$
 3 years ago

shadowfiend Group TitleBest ResponseYou've already chosen the best response.0
That's the first derivative, you can apply the same reasoning to get the second derivative, and then use julie's advice to find the shape of the function.
 3 years ago

shadowfiend Group TitleBest ResponseYou've already chosen the best response.0
(Feel free to correct me anyone  I'm doing this in my head and haven't gotten a chance to doublecheck myself.)
 3 years ago

MD Group TitleBest ResponseYou've already chosen the best response.0
One way of remembering the Chain Rule in this type of case is to remember that it will be the derivative of the outside function with the inside function left alone times the derivative of the inside function.
 3 years ago

MD Group TitleBest ResponseYou've already chosen the best response.0
So, in this case once you write the fucntion as, $$ (4+9x^{2})^{1}$$ the "outside function" is the outermost function, i.e. the exponent of "1" while the "inside function" is then $$4+9x^{2}$$, i.e. the stuff on the inside.
 3 years ago

MD Group TitleBest ResponseYou've already chosen the best response.0
We know that the derivative of say $u^{1}$ is $u^{2}$ so differentiating the outside, while leaving the inside alone would give, $$\left( 4+9x^{2}\right)^{2}$$ Then multiply all this by the derivative of the inside, $18x$. Or, putting it all together you get what shadofiend got.
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
wow thanks MD! very helpful. chain rule is a bit... confusing to decipher without explanation
 3 years ago

MD Group TitleBest ResponseYou've already chosen the best response.0
Yes, it's can be difficult when trying to learn it (or scape the rust off skills long unused :) ). If you recall the outside/inside function way of using the chain rule it can help with a lot of the "simpler" problems. Although I suspect "simpler" is in the eye of the beholder... :)
 3 years ago

mickey Group TitleBest ResponseYou've already chosen the best response.0
okay my text is working again
 3 years ago

julie Group TitleBest ResponseYou've already chosen the best response.0
@MD indeed! @mickey indeed!
 3 years ago

shadowfiend Group TitleBest ResponseYou've already chosen the best response.0
@MD Thanks  by the way, for inline LaTeX, I'm afraid you have to use \ ( and \ ) (without the spaces) so that we don't start messing up when people start using $ for money :) So \(u^{1}\) is \(u^{2}\) should work.
 3 years ago

MD Group TitleBest ResponseYou've already chosen the best response.0
Ah, I was wondering about that. It's been ages since I've seriously used LaTeX and I was thinking I'd misremembered how to do it (got a lot of rust there :) ). I'd forgotten about the other way of doing inline LaTeX. Thanks for reminding me! On a side note a preview button might be good when typing into the box directly, i.e without using the Equation editor....
 3 years ago

shadowfiend Group TitleBest ResponseYou've already chosen the best response.0
Yep. Ideally we'd like the equation editor itself to allow inline equations.
 3 years ago
See more questions >>>
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.