Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Check the hypotheses of Rolle’s Theorem and the Mean Value Theorem and find a value of c that makes the appropriate conclusion true. Illustrate the conclusion with a graph. f(x) = x^2 + 1, [2,-2]

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
Well, to satisfy rolle's theorem, you must satisfy the 3 conditions (you can find them in your book - if not, I can write them down for you if you don't have access to a book). Now to find the value of "c" using mean value theorem, you must start by finding the derivative of the function I'll leave you to find it's derivative as it is quite simple for this function. Basically, it must follow the first two conditions of rolle's theorem to apply the formula Then, plug it in to the formula: \[f'(c) = \frac{ f(b)-f(a) }{ b-a }\] on the given interval, which for your case it's -2
so find the derivative of x^2 + 1?
Yes. Find the derivative. Use the formula f'(c) = to solve for "c".

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

okay got you thanks
You don't need to check first two conditions since you know that your functions IS in fact continuous on the given interval and differentiable. So with that being said, best of luck.
@zepdrix can u help?
i did it but i think i got it wrong
f'(c) = f(-2) - f(2)/ -2 - 2 so f(-2) -2^2 + 1 = -3, f(2) 2^2 + 1 = 5. So the slope will be 2 because -3 - 5/-2-2 = -8/-4 which is 2. So To c : f'(x) = 2x, f'(c) = 2c = 2 2c = 2 so c will equal one (1) but when i checked (a< c
http://en.wikipedia.org/wiki/Rolle's_theorem
pick any two points ... on two sides of 0, you see that it satisfies the Rolle's theorem.
Did i go wrong when i found f'x? and find the f prime of c?
equate it to zero ... and you get x=0
your graph is symmetric f(-2) - f(2) should be zero ... probably you made mistake somewhere.
okay so c = to 0 right? i made a mistake in putting -2 and 2 ?
@zepdrix are u there?
@wio can u help
okay so its 0?
yes yes it is ..

Not the answer you are looking for?

Search for more explanations.

Ask your own question