Find the The Slopes of the tangent and the normal to the following curves at the indicated points :

Question

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

Philoid · Accepted Answer

Given:

xy = 56 at (1,6)

Here we have to use the product rule for above equation.

If u and v are differentiable function, then

(UV) = U + V

(xy) = (6)

⇒ x(y) + y(x) = (5)

(Constant) = 0

⇒ x + y = 0

⇒ x = – y

⇒

The Slope of the tangent at (1,6)is

⇒

⇒ = – 6

The Slope of the tangent at (1,6) is – 6

⇒ The Slope of the normal =