At what point does the graph of the function below have a minimum value?

Question

$x^{2} + 6 x + 8$ $x^2+6x+8$

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Answer 1 · 2018-05-24T12:39:31

$(- 3, - 1)$ $(-3,-1)$ minimum

Let $y y = = x^{2} + 6 x + 8$ $yy==x^2+6x+8$

$\frac{d y}{d x} = 2 x + 6$ $dy/dx=2x+6$

When $\frac{d y}{d x} = 0$ $dy/dx=0$ ,

$2 x + 6 = 0$ $2x+6=0$

Solve,

$x = - 3$ $x=-3$

When $x = - 3$ $x=-3$ ,

$y = {(- 3)}^{2} + 6 (- 3) + 8$ $y=(-3)^2+6(-3)+8$
$y = - 1$ $color(white)(y)=-1$

$:.(-3,-1)$ minimum

Graph:

graph{x^2+6x+8 [-10, 10, -5, 5]}