The coordinates for D are (-4, -7)
First we must locate point B as it is vital to finding the midpoint of BD. To do this, we take the average of the endpoints AC since B is its midpoint.
x values = -9 + 1 = -8
Then divide by 2 for the average -8/2 = -4
y values = -4 + 6 = 2
Then divide by 2 for the average 2/2 = 1
Therefore B must be (-4, 1)
Now we know the values of E must be the average of B and D. So we can write equations for each coordinate since we know they are averages.
x - values = (Bx + Dx)/2 = Ex
(-4 + Dx)/2 = -4 ---> multiply both sides by 2
-4 + Dx = -8 ---> add -4 to both sides
Dx = -4
y - values = (By + Dy)/2 = Ey
(1 + Dy)/2 = -3 ---> multiply both sides by 2
1 + Dy = -6 ---> subtract 1 from both side
Dy = -7
So the coordinates for D must be (-4, -7)
<span>18z-7(-3+2z)
= 18z + 21 - 14z
= 4z + 21
answer is False
</span><span>coefficient of z is 4, not 13</span>
The critical points are at x = 1 and x = 4 giving you the intervals (-inf, 1), (1, 4) and (4, inf).
By substituting x values in these 3 intervals, you can see that f'(x) is positive in the first and third intervals and negative in the second interval.
This means that f(x) is increasing in the first and third intervals and decreasing in the second interval.
The answer is D.
