1. The Mean Value Theorem works :In the equation f(x)=x^2 works in the Theorem in [0,2]
-*****It is both continuous and differentiable within that interval.
f(0)= 2 and f(2)=4, the MVT guarentees a point c in the interval.
f'(c) = f(2)-f(0)/2-0
2c = 4-0/2 = 2
c=1
2. The Mean Value Theorem only works for continuous and differentiable functions. When there are gaps, or when non-differentiable, as in the case of f(x) = sqareroot(x^2) + 3.
-This graph has a corner at x=0
-Non-differentiable
-There could not be any tangent lines throughout the graph.
