Given
The function,
[tex]g(x)=x^2+4x[/tex]
To find:
The maximum or minimum value of the function, and where does it occur.
Explanation:
It is given that,
[tex]g(x)=x^2+4x[/tex]
That implies,
Set g(x)=y.
Then,
[tex]\begin{gathered} y=x^2+4x \\ y=(x+2)^2-4 \\ y+4=(x+2)^2 \end{gathered}[/tex]
Here, a=1>0.
Then, the parabola opens up.
And, k is the minimum functional value, it occurs when x = h.
Therefore,
1) g(x) has a minimum value.
2) g(x)'s minimum value is -4.
3) And it occurs at x = -2.
