Question

Find all points (x,y) on the graph of y = x/(x-2) with tangent lines perpendicular to the line y=2x-1.

Answer 1

ok - so first:

what is the slope of y=2x-1?

then

what is the slope of a line perpendicular to it?

Answer 2

the slpe of y = 2x-1 would be m =2 and for a perpendicular line, the slope would be m =-1/2

Answer 3

ok

Now the tangent line of any curve has the slope of the derivative at that point

so you need to get an equation for the derivative of
y = x/(x-2)

(use the 'quotient rule')

Answer 4

so the derivative I got was -2/(x-2)^2

Answer 5

I haven't checked that - but assume it OK

So the points where the derivative are perp to the line are where the derivitiv = -1/2

SO make that equation and solve it

Answer 6

I'll check the derivitive

Answer 7

-2/(x-2)^2 = -1/2?

Answer 8

yes, if the derivative is correct

Answer 9

ok so I got x = 4,0

Answer 10

f'(u/v) = (u dv/dx - v du/dx)/ v^2

Answer 11

I meant -4

Answer 12

OK - I checked your differentiation and it is correct

so you have your answers - well done

Answer 13

I think it IS 0, 4 not 0,-4

Answer 14

yeah, you are correct

Answer 15

So - you did ALL that without any problem - what was your initial difficulty?

Answer 16

I was using the wrong slop, parallel slope instead of the perpendicular slope and I just wanted to also make sure I was doing every thing else correct...

Answer 17

oops wait a moment

I need to check - I think I missed a - sign...

Answer 18

I was setting the derivative equal to -2 instead of -1/2,
but I got the right answer so you were a very big help... thank you once again...

Answer 19

OK - if you're happy, I'll leave it as it is

Answer 20

OK - I see where I thought I'd gone wrong - but it was OK

The above answers are correct