How do you find a number c that satisfies the conclusion of the theorem for the function #f(x) = x^2 - 3x + 1# on the interval [-1,1]?

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Answer 1 · 2015-09-12T10:30:31

#c# is a solution to the equation #f'(x) = (f(1)-f(-1))/(1-(-1))#

For #f(x) = x^2 - 3x + 1# on the interval [-1,1]

We get:

#f'(x) = (f(1)-f(-1))/(1-(-1))#

#2x-3 = ((-1)-(5))/(1-(-1)) = (-6)/2 = -3#

So #x=0#

This is the only solution and is, of course in the interval mentioned in the conclusion of MVT. That is, it is in #(-1,1)#.

So the #c# we want is #c=0#.