NOTE: Figure not drawn to scale.

In the figure above, ABCD is a rectangle. Points A and C lie on the graph of *y* = *p**x*^{3}, where *p* is a constant. If the area of ABCD is 4, what is the value of *p* ?

Level of Difficulty E M

There are several things to make note of before beginning work on this problem: ABCD is a rectangle whose sides are parallel to the

Given the observations above, we can conclude that the rectangle is centered about the origin and that the magnitude of

Area = base x height; 4 = (1)(2

Therefore, 2 is the distance of the rectangle above and below the

Let's label point A with its coordinates: (-1/2, -2). This point must satisfy the cubic equation because it lies on the graph of that function. After plugging in:

-2 =

Solving for

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