Question

determine whether rolle’s theorem applies to the function on the interval. if it applies find all possible values of c

Answer 1

f(x) = |x-5| +3 on the inverval [-3,6]

To use the mean value theorem, we need 3 things

a. f(x) is continuous on [-3,6] which it is

b f(x) is differentiable on (-3,6) which it is not

The absolute value function has a problem at the vertex, which is at x=5. This is in our interval, so we can stop now

The mean value theorem does not apply since it is not differentiable at x=5