Hello, greghunter!

You've worked out the necessary information.

Curve has equation:

The point has coordinates (3,0) and lies on

Point also lies on , and the tangent at is parallel to the tangent at

Find the coordinates of

The derivative is: .

At

. . The slope of the tangent at is -7.

Where elseis the slope of the tangent equal to -7 ?

. . Solve: .

. .

So the tangent has slope -7 when (we know!) . . . and when

When

. . Therefore, the coordinates of are: .