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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