Which is the minimal value for the function f(x)=x^2+2x?

To calculate the extreme value for a function, minimum or maximum, we have to differentiate the function,which, in this case, is:

f'(x)= (x^2)' + (2x)'

f'(x)= 2*x + 2*1

f'(x)= 2x+2

Now, we'll calculate the root of the first derivative, this value being the value for the function f has the minimum value.

2x+2=0

2x=-2

We'll divide by 2:

x=-1

The minimum value of the function is

f(-1) = (-1)^2 + 2*(-1)

f(-1) = 1 - 2

f(-1) = -1