Question

Is the Mean Value Theorem applicable to the function f(x) = |x - 1| on the interval [0, 2]?

Why or why not?

Answer 1

The only point that derivative of the function f(x) = |x - 1| is not continuous is at x = 0. You need to check whether the slope for the interval (0,2) is continuous to see if you can apply MVT. The interval (0,2) does not include end points, so 0 is not in this interval. The function is continuous over the interval, so MVT can be applied.