The point $P(1,1)$ lies on $y=x^3$. Find the tangent at $P$. Show that its intersections with

Question

The point $P(1,1)$ lies on $y=x^3$. Find the tangent at $P$. Show that its intersections with the curve satisfy $$ (x-1)^2(x+2)=0. $$ Find the coordinates of the other intersection, $Q$.

Accepted Answer

(a) Tangent $y=3x-2$; (c) $Q=(-2,-8)$.

Differentiation

Differentiation