Question

Show that the points (0,0) and (sqrt 2pi, -sqrt 2pi) on the curve e^(x+y) = cos (xy) have a common tangent

Answer 1

i'd recommend using implicit differentiation to solve this one

Answer 2

find dy/dx at the two points. dy/dx should be equal to -1.

Answer 3

next, verify that the line y=-x includes both (0,0) and (sqrt(2pi),-sqrt(2pi))