Mean Value Theorem: find 'c' for f(x) = (x + 1)/x on [1/2,2]

[nicho240]

Verify that f(x) meets the requirements of the Mean Value Theorem and find c (if it exists) that meets these requirements: f(x)= (x+1)/x over [1/2, 2]

 

[skeeter]

Re: Mean Value Theorem

Verify that f(x) meets the requirements of the Mean Value Theorem and find c (if it exists) that meets these requirements: f(x)= (x+1)/x over [1/2, 2]

1. Is f(x) continuous over the interval [1/2, 2]?

2. Is f(x) differentiable over the interval (1/2, 2)?

3. If the answer to both questions above is yes, then use the following equation to solve for c ...

\(\displaystyle \L f'(c) = \frac{f(2) - f\left(\frac{1}{2}\right)}{2 - \frac{1}{2}}\)