koolkid11
3

# Determine whether there is a maximum or minimum vale for the given function, and find that value. f(x)= x^2+6x+4

Every second degree function has either a maximum (if a is negative) or a minimum (if a is positive). Our function, thus, has a minimum. The formula for it is: $(x, y)=(\frac{-b}{2a}, \frac{-\Delta}{4a})$ a is 1, b is 6, c is 4, $\Delta=b^2-4ac=36-16=20$, so the minimum is at coordinates (-3, -5), that is the function doesn't ever get below -5 and it gets there only when the argument is -3.