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## Homework Statement

For what values of a,m, and b does the function

satisfy the hypothesis of the Mean Value Theorem of the interval [0,2].{3 ,x=0

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

{mx + b ,1<=x<=2

## Homework Equations

(f(b) - f(a))/(b-a) = f'(c)

## The Attempt at a Solution

So, I wanted to make a point of continuity for the whole equation. So, I set the equation to x=1 in both cases and then equated them, and got;

2+a=m+b ---> a=m+b-2

Then, I found the derivative of the original equation and set x again to 1, then equated the two given that were diffable, and got;

m+b=1+a

Now I can't get any values for a,b, or m without getting:

3=0

I must be doing something wrong.