Mean Value Theorem - which values satisfy it question

htoor9
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Homework Statement



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

Homework Equations



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

The Attempt at a Solution



I am just really lost at what this is trying to ask...sorry :( I tried plugging in stuff in the equation but I'm really confused.
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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