Given the function f(x)=x/(x+9), how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,4] and find the c?

1 Answer
May 24, 2017

Please see below.

Explanation:

The Mean Value Theorem has two Hypotheses.
A hypothesis is satisfied if it is true.

H1: The function must be continuous on [1,4].

So, ask your self where f is NOT continuous. Are there any numbers in [1,4] where f is not continuous?

H2: The function must be differentiable on (1,4).

Find f' and determine whether there are any numbers in (1,4) where f' is not defined.

To (try to) find the c mentioned in the conclusion of the Mean Value Theorem,

set f'(x) = (f(4)-f(1))/(4-1) and solve the resulting equation.

Since the conclusion asserts the existence of a c in the interval (1,4) any solutions to the equation that are in the interval are values for c.