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**Rumor** Here's the problem:

"Find the x-coordinate of all points on the graph of $\displaystyle f(x)=-2x^3+2x+1$ where the tangent line is parallel to the line $\displaystyle y=-7x+2$."

I took the derivative of f(x) and got $\displaystyle f'(x)=-6x^2+2$. Then I set the slope of the line y equal to this equation, so as to have $\displaystyle -7=-6x^2+2$. So I solved for x and got $\displaystyle x^2=-(9/6)$ and so x=1.225 (after taking the square root).

I went ahead and found the actual tangent line of this by plugging that x-value back into the derivative of f(x), ending with $\displaystyle y=-7(x+1.225)+7$.

I'm pretty sure I did the process right, but if I didn't, could someone kindly correct me? Or tell me if I'm leaving something out? I feel like there's something else that should be done.