Consider the function graphed below.
graph of a piecewise linear function from on the interval [a,b].  let L=(b-a)/3.  the function extends from (a,0) to (a+L,2) to (a+2L,2.5) to (b,1.5).  x=m is between x=a and x=a+L, x=n beween x=a+L and x=a+2L, and x=p between x=a+2L and x=b.

Does this function satisfy the hypotheses of the Mean Value Theorem on the interval ?

Does it satisfy the conclusion?

At what point is ?