Two different tangents which are perpendicular?

[razored]

Homework Statement

Does the curve y=x^2 have two different tangents which are perpendicular? Does the curve y=x^3?

The Attempt at a Solution

I have no idea how to prove that for x^2 or x^3.
(x^2)' =2x that is tangent at a point x
then m = -1/2 x for another point...
How do i prove that there is sucha point? then how about x^3?

 

[HallsofIvy]

Two lines are perpendicular if and only if the product of their slopes is -1. So the question is, "are the two different values of x, say x1 and x2, such that (2x1)(2x2)= -1?"
For the cubic, the corresponding equation is (3x1²)(3x2²)= -1.