Question

Find the slopes of the tangent and the normal to the curves at the indicated points: xy = 6 at (1,6)

Answer 1

Given as xy = 6 at (1,6)

Differentiate using product rule

Slope of tangent at (1,6) is 

dy/dx = -6/1

dy/dx = -6

Slope of tangent at (1,6) is -6

Slope of normal = -1/slope of tangent

= -1/(dy/dx)

= -1/-6

= 1/6