Thread: Calculus--Mean Value Theorem (May only need help w/ the algebra?)

Here's the problem:

The value c that satisfies the conclusion of the Mean Value Thm for the function x/(x+2) on the interval [1,4] is:

A) 2

B) -2 + 3sq rt(2)

C) no such c exists

D) -2 + 2sq rt(6)


First, I know to find the derivative: 2c + 2/(c+2)^2

Then, I find f(b) - f(a)/(b-a) which equals 1/9

Then, I set 1/9 or f'(c) equal to the derivative which is 2c + 2/(c+2)^2

so, I end up with 2c + 2/(c^2 + 4c + 4) = 1/9

If I have done all of this correct up until this point, my only problem really lies within the algebra to solve for c in the above equation. Can anyone please help? (Would be great if someone could show me the algebra steps to find c) Thanks!

Originally Posted by obsmith08

Here's the problem:

The value c that satisfies the conclusion of the Mean Value Thm for the function x/(x+2) on the interval [1,4] is:

A) 2

B) -2 + 3sq rt(2)

C) no such c exists

D) -2 + 2sq rt(6)


First, I know to find the derivative: 2c + 2/(c+2)^2 (**)

Then, I find f(b) - f(a)/(b-a) which equals 1/9

Then, I set 1/9 or f'(c) equal to the derivative which is 2c + 2/(c+2)^2

so, I end up with 2c + 2/(c^2 + 4c + 4) = 1/9

If I have done all of this correct up until this point, my only problem really lies within the algebra to solve for c in the above equation. Can anyone please help? (Would be great if someone could show me the algebra steps to find c) Thanks!

How did you get the derivative in (**) above?

Originally Posted by danny arrigo

How did you get the derivative in (**) above?

Whoops, that might be my first problem! the sign in the numerator should have been negative instead of positive making the derivative: 2/(x+2)^2 or 2/(x^2 + 4x + 4)

Thank you for pointing that out! I'm going to see if this makes solving for c any easier...

Originally Posted by danny arrigo

How did you get the derivative in (**) above?

Thank you for pointing out my careless mistake! I think that's all the help that I needed.... Once I found the correct derivative it made solving for c much easier! I got -2 + 3sq rt(2)

Thanks!