posted by cal .
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
y(x) = 6x/(x-9)^2
when i workout this problem I get this:
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 xâ‰ 9 , there is a vertical asymptote at x=9
x = 11
but I have these answer choices to choose from:
A. x=9 and x=6
C. x=-9 and x=6
D. x= 6
E. The graph has no horizontal tangents.
is it E then
you lost an x there when factoring out the 6(x-9)
y' = -6(x+9)/(x-9)^3
y'=0 at x = -9