Question

Find the equation of both the tangent lines to the curve y=x^3-x that are parallel to the line 22x-2y+1=0

Answer 1

is this geometry??

Answer 2

No. It's calculus

Answer 3

damm im not really familiar with it but i can try to hlp

Answer 4

jus tell me ur main problem and ill see wat i can do

Answer 5

Well, I'm sure to get the equation... I just don't know how to approach this question. I tried to differentiate both tangent lines...

Answer 6

not sure *

Answer 7

do u hve any notes that u can use??

Answer 8

how are you going with this? still need help?

Answer 9

Yes, I still need help

Answer 10

so the 2 tangent lines must have the same slope as 22x-2y+1=0
do you know what the slope of this line is?

Answer 11

So take the derivative of the 22x-2y+1=0?

Answer 12

No. first we re-arange the equation
22x+1=2y
y=11x + 1/2
so what do you think the slope might be?

Answer 13

11

Answer 14

that's it!
so we're looking for two tangent lines with a slope of 11
i.e. y=11x+b

now we take the derivative of y=x^3-x

what do you think that would be?

Answer 15

y'=3x^2-1

Answer 16

that's right

so now we need to know at what values of x that this derivative (or slope of the tangent) is equal to 11

i.e. 3x^2 - 1 = 11

Answer 17

see if you can find the 2 values of x

Answer 18

Is it +/-2?

Answer 19

very good.

the tangent lines touch the cubic at x=2 & x=-2

so now we need to know the corresponding y-values using the original cubic equation.

what would they be?

Answer 20

Is it y=6 and y=-6?

Answer 21

well done!

so know we can work out the two tangent equations y=11x+b
by substituting these two points and evaluating b

Answer 22

Oh I see! I think I got it from here!

Answer 23

I got these two equations:
11x-y-16=0 and 11x-y+16=0

Answer 24

yep you got it.
can also be written as y=11x+16 and y = 11x-16

Answer 25

Okay! Thank you so much! :)

Answer 26

your welcome