Question

What is the equation of the line normal to `f(x)=-x/(x+4)` at `x=6`?

Answer 1

y = 25 x `-`753/5.

Explanation:

Denoting f(x) by y, the equation simplifies to `-`1 + 4 / ( x + 4 ).
The point under reference is P ( 6, `-`3/5 )
`d/dx`y = `-`4 / ( x + 4 )^2.
The slope of the normal at P is `-`1 / `d/dx`y at P = 25.
So, its equation is y + 3/5 = 25 ( x `-`6 )..