determine whether there is a max or a min value for the given function, find that value:

f(x)= x squared -7x +6

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f(x) = x^2 - 7x + 6

First we need to obtain the first derivative's zeros:

f'(x) = 2x - 7 = 0

==> 2x = 7

==> x= 7/2

Now we have a critical values at x= 7/2 which means the the function f(x) has a minimmum values at f(7/2)

==> f(-3) = (7/2)^2 - 7(7/2) + 6

= 49/4 - 49/2 +6 = (49-98+24) / 4 = -25/4

Then the minnimum value is:

f(7/2) = -25/4 OR the point (7/2,-25/4)

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