Question

For what value of c is the curve y=c/(x+1) tangent to the line through the points (0,3) and (5,-2)?

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

so i know y'=(x-c+1)/(x+1)^2
and i know the line of that tangent line has slope -1
and i was thinking i set them equal to each other but then i get
x^2+x+c=0
the discrimnant is -b-4ac=1-4(1)c
we want the discrimnant to be zero so we have one unique tangent line right?
so we have 1-4c=0
this implies c=1/4

Answer 3

but the back of the book has 4

Answer 4

ok the slope of the line is -1, but i think \[y'=\frac{-c}{(x+1)^2}\]

Answer 5

you are right

Answer 6

now if you set = -1 i bet you get the right answer

Answer 7

so that is the correct way i mentioned above?

Answer 8

just set the discriminant =0?

Answer 9

think so let me check

Answer 10

hmmm x=-1+ or - sqrt{c}
don't know how to get 4 from this

Answer 11

oh wait. the curve has to be tangent to the line, so i must touch the line yes?

Answer 12

the line must touch the curve yes!

Answer 13

so we are trying to find the intersection so maybe i should find the line of the tangent line and set it equal to the curve y=c/(x+1)?

Answer 14

so if my thinking is correct we have two equations, \[(x+1)^2=c\] and
\[\frac{c}{x+1}=-x+3\]

Answer 15

the first from the derivative being -1 and the second because for that value of c the line which is y = -x+3 must intersect the curve

Answer 16

how did you get y=-x+3?

Answer 17

so we geet
\[(x+1)^2=(x+1)(-x+3)\]

Answer 18

oh line w/ slope -1 through (0,3)

Answer 19

oh duh nvm

Answer 20

you've got the slope and the y intercept.
i think this gives
\[x+1=-x+3\]
\[2x=2\]
\[x=1\] but apparently that is not the answer so let me try again

Answer 21

so i get x=1 and x=-1 from that
if x=1
then x=(1+1)^2=2^2=4
but
if x=-1
then x=(-1+1)^2=0^2=0

Answer 22

those are suppose to be c
i accidently wrote x again sorry

Answer 23

x=1
c=(1+1)^2=4
x=-1
c=(0)^2=0

Answer 24

oh right! i solved for x and forgot we were looking for c. duh

Answer 25

gj thanks satellite
remember that is my bike

Answer 26

nope

Answer 27

amistre gave it to me

Answer 28

yeah, but as you can see i stole it

Answer 29

satellite do you know who i am?

Answer 30

nope? myininaya?

Answer 31

lol i didn't wanna seem like a retard asking it has the goddess myininaya

Answer 32

as*

Answer 33

ho ho ho ho ho ho

or as we say here lol

Answer 34

lol

Answer 35

glad it was me that caught this one!

Answer 36

now i can retire for the night

Answer 37

good night satellite
thanks for showing me my error
and i totally forgot to set those lines/curves equal
you're the best

Answer 38

no you are!

Answer 39

no you!