How do you find the value of c guaranteed by the Mean Value Theorem for #f(x)=(2x)/(x^2+1)# on the interval [0,1]?
1 Answer
Explanation:
I would begin by checking that the hypotheses are true.
This function is continuous on
and differentiable on
so the hypotheses of the Mean Value Theorem are true.
The conclusion of the Mean Value Theorem is that there is a number
We have been asked to find the number(s) whose existence the theorem asserts.
For
Furthermore
We need to solve:
So
Complete the square or use the quadratic formula to solve for
Clearly
Again clearly, the negative root is not in