1). To be perpendicular to y=x which has a slope of 1 the tangent of the curve must have a slope of -1
dy/dx=(x+2-x-3)/(x+2)^2
dy/dx=-1/(x+2)^2
dy/dx must equal -1 to be perpendicular to y=x
-1/(x+2)^2=-1
-1/(x^2+4x+4)=-1
-1=-x^2-4x-4
x^2+4x+3=0
x^2+x+3x+3=0
x(x+1)+3(x+1)=0
(x+3)(x+1)=0
x=(-1, -3)
2). y = x + 3/x + 2
Plots: x from - to - 1.6
Plot: x from - 6 to 1.4
Alternate Form:
y = 1/x + 2 + 1
(x + 2) y = x + 3
Expanded form:
y = x/x + 2 + 3/x + 2
Root: x = - 3
Limit:
3 + x/2 + x = 1
