Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
verify that the hypothesis of the Mean value theorem are satisfied on the given interval and findall values of c that satisfy theconclusion of the theorem.
f(x)=x^2+x [4,6]
 one year ago
 one year ago
verify that the hypothesis of the Mean value theorem are satisfied on the given interval and findall values of c that satisfy theconclusion of the theorem. f(x)=x^2+x [4,6]
 one year ago
 one year ago

This Question is Closed

zepdrixBest ResponseYou've already chosen the best response.1
Do you understand how the MealValue Theorem works? :O
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
hm.. i'll try to do this one myself and ask for help if i still can't get the answer :)
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1358281444723:dwOk but here's a brief explanation of the concept c: just in case it helps.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Remember the formula for finding the slope of a line between 2 points? (a secant line) If we use the notation from the graph,\[\large m=\frac{f(b)f(a)}{ba}\] In order for the function to be continuous, this slope must be equal to the slope of a TANGENT line somewhere in the middle.\[\large \frac{f(b)f(a)}{ba}=f'(c)\] A derivative at a particular point represents the slope of a tangent line.
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
ok, i need help... i dont know how to do this.. haha i thought i did but i dont. so, please continueee :)
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
So in this problem we're starting with a secant line, passing through x=4 and x=6. Let's start by finding the slope \(m\) of that line.\[\large m=\frac{f(6)f(4)}{6(4)}\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large m=\frac{\color{orangered}{f(6)}\color{cornflowerblue}{f(4)}}{6(4)}\] \[\large m=\frac{(\color{orangered}{6^2+6})(\color{cornflowerblue}{(4)^24})}{6+4}\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Understand how those got plugged in?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Simplifying that down, I think we end up withhhhhhhhh 3ish.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
So the theorem says  In order for this function to be continuous from 4 to 6, there must be a TANGENT line somewhere between those points that has this slope of 3.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Let's first find f'(x).
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
So then,\[\large f'(c)=2c+1\]And we're claiming, that by the MeanValue Theorem this tangent line at x=c has a slope of 3. It has to happen somewhere between 4 and 6 in order for the function to be continuous. So let's set our f'(c) equal to 3 and solve for c. \[\large 2c+1=3\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
When you get an answer, verify whether or not it is BETWEEN 4 and 6. Because that will help to verify that we didn't make a mistake somewhere.
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
since it's 1, it is between 4 and 6 :)
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
yes. but is that the final answer? i thought we were supposed to use the mean value theorem.. which says: if F is continuous on [z,b], and if F is an antiderivative of F on [a,b], then \[\int\limits_{a}^{b}f(x)dx=f(b)f(a)\].
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
oops, i meant [a,b]..
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Oh crap maybe i confused it with the intermediate value theorem... sec.. thinking :3
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
ahh darn. haha ok ;p
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
hmm no it doesn't appear i did... hmmmm
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
The thing you posted is the FTC (Fundamental Theorem of Calculus, Part 2).\[\large \int\limits_a^b f(x)dx=F(b)F(a)\] I'm not quite sure what that has to do with the mean value theorem D: hmmm
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
oh sorryyy yea thta IS the fundamental theorem of calculus.. ha but the mean value theorem of integrals says : if f is conb], then there exists at least one number x* in [a,b] such that \[\int\limits_{a}^{b}f(x)dx=f(x*)(ba).\]
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
if f is continuous on [a,b] i meant.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Hmm crap I dunno D: I'm familiar with seeing it that way.
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
aw darn it.. is there anyone you could ask help for? because that formula is what my teacher uses... :'(
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
@hartnn @hba @campbell_st Maybe one of these fellas know what you're talking about c:
 one year ago

mlddmlnogBest ResponseYou've already chosen the best response.0
oh nvermind! we got the correct answer. so i';lljust do it the way @zepdrix did it! :D thank you for comming anyway! :)
 one year 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.