Question

Find the acute angle between the curves at their points of intersection y=x^2 and y=x^3

Answer 1

Hello,

First let's find the points of intersection:

x^3=x^2==>x^3-x²=x²(x-1)==>x=0 or x=1
(x²)'=2x
(x^3)'=3x²

If x=0 then y=0*x+0 is a commun tangent of the 2 curves.
==> angle=0°

if x=1 then
tan a=2 and tan b=3
angle=arctan 3-arctan 2=8.130120....°