find the minimmum value for f(x) = x^2 + 6x -5

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f(x) = x^2 + 6x - 5

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

f'(x) = 2x + 6 = 0

==> 2x = -6

==> x= -3

Now we have a critical values at x= -3 which means the the function f(x) has a minimmum values at f(-3)

==> f(-3) = (-3)^2 + 6*-3 - 5

                 = 9 - 18 - 5 = -14

Then the minnimum value is:

f(-3) = -14   OR the point (-3,-14)

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