Given the function #f(x)=(-x^2+9)/(4x)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,3] and find the c?
2 Answers
The only hypothesis required by the mean value theorem is that
Explanation:
The only hypothesis required by the mean value theorem is that
As:
is in fact continuous in
We can calculate the definite integral as:
Then we can find
I will assume that you are referring to the Mean Value Theorem for Derivatives.
Explanation:
You determine whether it satisfies the hypotheses by determining whether
You find the
Therefore this function satisfies the hypotheses of the Mean Value Theorem on this interval.
To find
You should get