I went in to my professor for "extra help" on this problem and left more confused than before I went in.

Can someone on here try to explain this to me!

Question:

For what values of a, m, and b does the function satisfy the hypotheses of the Mean Value Theorem on the inverval [0, 2]

Piecewise function:

f(x)= 3, x=0

f(x)=-x^2 + 3x + a, 0<x<1

f(x)=mx + b 1</= x </= 2

Thank you so much for any help!