# Help with Mean Value Theorem

• Jul 26th 2009, 01:25 PM
E.L.Kim
Help with Mean Value Theorem
Hey everyone. I first found this forum and thought I'd love to help some people, but it turns out that that will have to wait until I get this problem done. *sigh* It isn't going well. Basically, I don't know what my professor is asking for (hopefully this isn't a duplicate or in a wrong forum. I looked around and thought this would be best):

Use the Mean Value Theorem for Derivatives to approximate the slope of the function:

f(x) = x^3 + 2x + 1 where c = 1.3.

The hint she gave us was confusing (maybe because of proper grammar, not sure). Here it is:

Solve for the derivative, and then approximate it by using at least 3 different intervals.... ie., 3 choices of (a,b) which allow you to approach the exact value of the derivative.

There was nothing like this in the text. We studied the Mean Value Theorem for Derivatives but all the examples were on how to find C. Now, we are given C and being asked for... what? Can someone walk me through this? The professor refuses to answer questions. It's due pretty soon, though I got the first part of the assignment (Newton's Method) done and I could probably submit that and ask for more time on this.

Thanks!
Elaine.
• Jul 26th 2009, 01:49 PM
VonNemo19
Quote:

Originally Posted by E.L.Kim
Hey everyone. I first found this forum and thought I'd love to help some people, but it turns out that that will have to wait until I get this problem done. *sigh* It isn't going well. Basically, I don't know what my professor is asking for (hopefully this isn't a duplicate or in a wrong forum. I looked around and thought this would be best):

Use the Mean Value Theorem for Derivatives to approximate the slope of the function:

f(x) = x^3 + 2x + 1 where c = 1.3.

The hint she gave us was confusing (maybe because of proper grammar, not sure). Here it is:

Solve for the derivative, and then approximate it by using at least 3 different intervals.... ie., 3 choices of (a,b) which allow you to approach the exact value of the derivative.

There was nothing like this in the text. We studied the Mean Value Theorem for Derivatives but all the examples were on how to find C. Now, we are given C and being asked for... what? Can someone walk me through this? The professor refuses to answer questions. It's due pretty soon, though I got the first part of the assignment (Newton's Method) done and I could probably submit that and ask for more time on this.

Thanks!
Elaine.

First find $\displaystyle f'(c)=7.07$

Then from the MVT, you know that $\displaystyle 7.07=\frac{f(b)-f(a)}{b-a}$ for some interval $\displaystyle [a,b]$ containing $\displaystyle c$.

What I would do is chose $\displaystyle a=1$, $\displaystyle b=2$ and see what happens.

ie...$\displaystyle 7.07=\frac{[(2)^3+2(2)+1]-[(1)^3+2(1)+1]}{2-1}$

Do it again for values convinient for yourself. Remeber that your quotient needs to be "about" 7, so try to "eyeball" the next values you choose with this in mind. It would be a real good idea to look at the graph!