Question

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.

y(x) = 6x/(x-9)^2

Answer 1

by quotient rule:

dy/dx = ( (x-9)^2 (6) - 6x(2)(x-9))/(x-9)^4
= 0 at a horizontal tangent

6(x-9)^2 - 12x(x-9) = 0
6(x-9)[x-9 - 2] = 0
6(x-9)(x-11) = 0
x=9 or x=11 , but x≠9 , there is a vertical asymptote at x=9

x = 11

Answer 2

I have these answer choices:

x=9 and x=6

x=-9

x=-9 and x=6

x= 6

The graph has no horizontal tangents.