Describe the slope of the tangent line to the curve defined by x 2 + xy - y 2 = 5 when x = 2.

Question

positive

negative

zero

undefined

Answer 1

2 x dx + x dy + y dx - 2 y dy = 0

dy ( x-2y) = - dx ( 2x + y)

dy/dx = (2 x + y)/(2y-x) = slope

at x = 2
4 + 2 y - y^2 = 5
y^2 - 2 y + 1 = 0
(y -1)^2 = 0
y = 1
so
dy/dx = (5)/0 undefined