DavidUsa
  • DavidUsa
Can someone explain the mean value theorem to me?
Calculus1
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
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.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Psymon
  • Psymon
So, Im sure you have a formula for this in a textbook somewhere or in notes. Ill write it down and then see if we can explain what it is telling us: \[f'(c) = \frac{ f(b)-f(a) }{ b-a } \] So let's explain the f'(c) part first.
Psymon
  • Psymon
So first off, f'(x) just means derivative. C is usually always meant to mean a constant, just some number. So f'(c) means we take the derivative and then plug in a point. Now just saying that gives us no context, though. So what a derivative does is give us an equation for slope. When you take the derivative of a function, you can plug in any x-coordinate and get the slope at that x-coordinate. So for a quick example, if I have a function 3x^2 and I want to know the slope at the point (2,12) I do this. I take the derivative to get 6x. Then I plug in the x-coordinate of 2. Doing that gives me 12. 12 is the slope of the graph of 3x^2 when x = 2. So basically, f'(c) means the slope at some point on a graph. That make sense so far?
anonymous
  • anonymous
|dw:1377856206781:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
so @Psymon formula also works for a straight line. In terms of calculus, all the integral is saying is the sum of the value of the function on the y axis at all points between the limits. The part outside the integral (ie the 1/(b-a)) is the inverse of the length over which the sum of all y values on the function has occurred. Thus we are getting the sum of all functions between 2 points and dividing this answer by the length. This is the average value of the function.
Psymon
  • Psymon
Did I do something wrong or confusing in what I was trying to explain? I was just going through mean value theorem, not average value. Anyway, if they're asking about MVT then I doubt theyve seen much of anything about integration yet. Unless there some flaw in what I was doing, not sure what in particular you were trying to point out to me O.o
anonymous
  • anonymous
@psymon I was not trying to point out anything to you personally, I saw the question and have never heard of mean value theorem. Mean value, average value. It's the same thing for a linear equation.

Looking for something else?

Not the answer you are looking for? Search for more explanations.