Answer:
(a) y = 9/4x -1/4
(b) (-2, -2), (-2, 2)
(c) see below
Step-by-step explanation:
(a) The derivative can be found from ...
2y·y' = 3x² +6x
At (x, y) = (1, 2), this is ...
4y' = 9
y' = 9/4
so the equation of the tangent is ...
y = (9/4)(x -1) +2
y = (9/4)x -1/4
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(b) At y' = 0, we have ...
0 = 3x² +6x = 3x(x +2)
This says y' = 0 at x=0 or x=-2. (x = 0 is an extraneous solution.)
At x = -2, we have ...
y² = (-2)³ +3(-2)² = -8+12 = 4
y = ±2
So, the horizontal tangent points are (x, y) = (-2, ±2).
The equation would be ... Y = 2x + (-5)
Answer:
I believe it would be option B.
Step-by-step explanation:
72 people stayed, because 96 ÷ 4 = 24, and 24 * 3 is 72.
It will help to graph it, so that you can see the shape. However, you can also just solve it by looking at the vertices. If you graph it, you'll see that the shape is a trapezoid. The two bases are 4 and 6, while the height is 5 - 1 = 4. So, we solve by using the equation for the area of a trapezoid: (6 + 4) * 4 * .5 = 20 units squared.