Gverify that the mean value theorem applies to f(x)= x+2/x on the interval [1,2] find point c satisfying conclusion

The mean value theorem requires that a function is continuous on the interval and differentiable on the same open interval .

Since the only point of discontinuity of your function is , where the denominator of 2/x equals zero, the function is defined, continuous and differentiable on the interval .

Since the hypothesis of the mean value theorem are verified, we can claim that there exists a point such that

In your case, , so the expression becomes

Let's compute the derivative:

So, we're looking for a point c such that

Since we are looking for a point in , we accept the solution