Question

At what point on y=(-3)/(x-1) does the tangent pass through the origin? Helpp!!!

Answer 1

First question: are you in calc 1?

Answer 2

yeah i think lol high school calculus

Answer 3

Same thing.

Answer 4

Anyway, I am going to assume you guys are learnign about derivatives, correct?

Answer 5

yep i found the derivative but idk what else to do afterwards

Answer 6

So what technically (in case if your teacher did not make this clear), a derivative of a curve, is technically the slope, so to speak.

Answer 7

So if you were to, i dont know, set it up in some sort of linear function using your (0,0) point I would imagine you could find an equation. :D

Answer 8

0=m(0)+b, solve for b.

Answer 9

hmm ok ill try it

Answer 10

Make sense?

Answer 11

but the thing is i have to find the point

Answer 12

Hold on, comp acting funny

Answer 13

Ah i see what you're asking.

Answer 14

y =(-3)/(x-1)
So
y ' = 3/(x-1)^2
let the point of tangency (a, y(a)) ==> (a, (-3)/(x-1)))

Answer 15

So the sloope at that point will be 3/(a-1)^2

Answer 16

ok

Answer 17

So the equation of tangent with slope 3/(a-1)^2 and passing through (a, (-3)/(x-1)) is
y -(-3)/(x-1)= 3/(a-1)^2* (x - a)

Answer 18

Since (0,0) is a point in this line you can substitute 0 for x and 0 for y.

Answer 19

So we have 3/(-1)=3/(a-1)^2*(-a)

Answer 20

-3=(-3a)/(a-1)^2
-3(a-1)^2=-3a
-3(a^2-2a+1)=-3a
a^2-2a+1=a
a^2-3a+1

Answer 21

=0*

Answer 22

Hmmmm

Answer 23

In theory that should have worked... where did i make an algebraic mistake?

Answer 24

ok ill try do it the same way u did

Answer 25

And hopefully you dont run into the error i am running into. This is strange.

Answer 26

ok i got the answer thank you so much for pointing out what to do i have a test tomorrow and i was literally freaking out so ur a lifesaver

Answer 27

Well, I am happy to hear my idea pushed you the right direction.

Answer 28

Also, some pointers on calc in high school (thats when I took it):

Answer 29

Breathe and practice similar problems =D

Answer 30

Did the process make sense?

Answer 31

yep it did and besides i got the correct answer :)

Answer 32

Yay! Well I wish you luck on your exam, be sure to get some sleep (always a good thing).

Answer 33

thanks a lot

Answer 34

You're welcome.