Find the number c that satisfies the conclusion of the mean value theorem on the given interval. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.) f(x) = x , [0, 9]

Step-by-step explanation:

The following information is missing in the given question:

Using this we may solve the question as:

We are given the following in the question:

We have to find the number c such that f(x) satisfies the Mean value theorem.

Mean Value theorem:

It states that if the function is differentiable in the closed interval [a,b], differentiable in the interval (a,b), then there exist c in (a,b) such that:

Now,

Continuity in [0,9]

Since a polynomial function is continuous everywhere, f(x) is continuous in [0,9]

Differentiability in (0,9)

Since a polynomial function is differentiable everywhere the given function is differentiable in interval (0,9)

Then, by mean value theorem: