y=-x^2-6x
interval when function is increasing?
interval when function is decreasing?

Question

y=-x^2-6x
interval when function is increasing?
interval when function is decreasing?

anonymous · Answer

The derivative is

$$y \prime = -2x-6$$

When $$y \prime > 0$$
The function is increasing

If $$y \prime < 0$$

The function is decreasing, then?...

anonymous · Answer

The derivative changes in x=-3

So is increasing in the interval$$(-\infty, -3)$$
(Because y'>0 or positive)
and decreasing in 
$$(-3,\infty)$$
(because y' is negative)

anonymous · Answer

Thank you.. how to do I fiqure out the vertex

anonymous · Answer

Complete the polynomial, to find the vertex

anonymous · Answer

$$y=-x ^{2}-6x$$
$$y=-(x ^{2}+6x)$$
Rounding out the perfect square trinomial (I used google traductor)
$$y=-\left[ \left( x+3 \right)^{2}-9 \right]$$
$$y=-(x+3)^{2}+9$$
$$y-9=-(x+3)^{2}$$
From this equation we can gen the vertex V(-3,9)