...Determine the equation of the line that passes through the point (2,2) and is perpendicular to the tangent to y=2x-3x^3 at x=-1.

To solve this first would I use the difference quotient on y=2x-3x^3 to find the slope of the tangent?

that would be a good start if you can't take the derivative directly using the power rule.

And why can't I graph y=2x-3x^3 on my graphing calculator?

what instructions were you given? is use of a calculator permitted for this problem?