Mean Value Theorem question help

[ATamcsu]

Im really with this question and dont really understand what to do, can someone explain this?:

 

[Deleted member 4993]

Im really with this question and dont really understand what to do, can someone explain this?:View attachment 15574

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Starting with the definition of mean-value theorem (mathematically).

 

[ATamcsu]

Oh ok so i know the formula f'(c) = f(b) - f(a) / b - a. Once i plug in b and a, i get 0? and then how do i solve for "c" once i set the derivative of the equation equal to zero?

 

[Dr.Peterson]

Im really with this question and dont really understand what to do, can someone explain this?:View attachment 15574

If your textbook or notes do not provide any examples like this, try this site: http://tutorial.math.lamar.edu/Classes/CalcI/MeanValueTheorem.aspx

That states the theorem, and gives a simple example like yours (example 2).

Once you know what you are supposed to do, give it a try and show us your work, even if you know it's wrong.

 

[ATamcsu]

Is this right?

 

[Steven G]

Looks good to be.
In your earlier post you wrote f'(c) = f(b) - f(a) / b - a which means \(\displaystyle f'(c) = f(b)-\dfrac{f(a)}{b}-a\) which clearly is not the correct formula. Use parenthesis!

 

[HallsofIvy]

Oh ok so i know the formula f'(c) = f(b) - f(a) / b - a.

I was going to say "No, f'(c)= (f(b)- f(a))/(b- a)" but Jomo beat me to it!