These are two different types of max min problems but I understand that they go on a graph instead of being the usual rectangle with a given value question.
For the first:
two lines are parrallel if they have the same slope. the slope of the line is 9. so we simply want to find the $\displaystyle x$'s that make the tangent lines to the curve have a slope of 9. the derivative gives the formula for the slope of the tangent line.
$\displaystyle y = x^3 - 3x^2$
$\displaystyle \Rightarrow y' = 3x^2 - 6x$
Now we simply solve:
$\displaystyle 3x^2 - 6x = 9$
i leave that to you
see http://www.mathhelpforum.com/math-he...ma-minima.html as a hint for the second
i assume you remember how to maximize a function
we want two points ON THE CURVE, therefore you would plug them into the original function to obtain the y-values for the points. we wouldn't sub them into the line, unless we knew that the line intersected with our curve exactly at the points where the slope of the curve is 9. so just plug them into $\displaystyle y = x^3 - 3x^2$
why did you think you would plug it into the line?