Question

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, 25]

Answer 1

Answer:

c is all the points in the open interval (0,25)

Step-by-step explanation:

Here given is a function

$f(x) =x$, which is continuous  in the interval [0,25] and differentiable in (0,25)

Mean value theorem says there exists at least one c in the interval (0,25) such that

$f'(c) = \frac{f(25)-f(0)}{25-0}$

We have

$f(25)=25 and f(0) = 0\\f'(c) = 1$

For the given function

$f'(x) =1$

Hence we have c equals all the points in the open interval (0,25)