The question I have been struggling with is
Find P on the curve y-x^3 such that the slope of the line passing through P and (1,1) is 3/4
Another way of doing this: a line passing through (1, 1) with slope 3/4 is of the form y- 1= (3/4)(x- 1) or y= (3/4)x+ 1/4. Solve that and $\displaystyle y= x^3$ simultaneously. Just replacing y in $\displaystyle y= x^3$ with (3/4)x+ 1/4 gives a cubic equation with a simple answer.