Question

Find the point at which f(x)= x/(sqrt(9x-1) has a horizontal tangent line.
x=?

Answer 1

find 1º derivative and make it equal to 0. Solve that for x

Answer 2

But because there are two x's do I have to use the qoutient theorem first?

Answer 3

I came up with -1/2x(9x-1)^(-3/2)

Answer 4

Then I came up with ((-9/2x)^2+(1/2x))^(-3/2)=0

Answer 5

x=2/9 as dy/dx=0

Answer 6

how did you find that?

Answer 7

dy/dx=squareroot (9x-1)(1) -x*1*9/2*square root(9x-1) whole divided by (9x-1) =0 {as tangent horizontal dy/dx=o}
c this is the quotient rule that we have applied and simplifying
we get x=2/9

Answer 8

if u like the result then let's chat i m feeling quite bored after long hours of studying....................................