The relative minimum of the function f(x) = x(x+5) is at x = -5/2.
To find the relative minimum of the function f(x) = x(x+5), we can use the first derivative test.
First, we find the first derivative of f(x) with respect to x:
f'(x) = 2x + 5
Next, we set f'(x) = 0 to find the critical points:
2x + 5 = 0
x = -5/2
Since f'(x) is always positive for x < -5/2 and always negative for x > -5/2, we know that x = -5/2 is a relative minimum of f(x).
Therefore, the relative minimum of the function f(x) = x(x+5) is at x = -5/2.