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

To calculate the local extremes of a function, minimum or
maximum, we'll do the first derivative test. 

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

f'(x) = 2x + 6

Now,
we'll calculate the roots of the first derivative. Each root of derivative represents
the value for the function f(x) has an extreme value.

f'(x)
= 0

2x + 6 = 0

We'll factorize
by 2:

2(x+3) = 0

We'll divide
by 2:

x + 3 = 0

We'll subtract
3 both sides:

x = -3

Now,
we'll calculate the minimum value of the function:

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

f(-3) = 9 - 18 -
5

f(-3) =
-14

The coordinates of the minimum point are:
(-3 , -14).