Let P be a point on the graph of y = x3. The tangent line at P will intersect the graph at the point Q. (a) If P has x-coordinate a, then what is the equation of the tangent line at P: y= x+ (b) The line in (a) will intersect the curve y = x3 in two places; one of these is P and the other point is: ) Hint: This part involves factoring a cubic in x. In general, this may be difficult. However, in this case since we know point P is an intersection point, x=a must be a solution, so x-a must be a factor. You should now be able to f (c)The ratio of the slope of the curve at Q to the slope at P is