Question

For the curve f(x)=2x^2-2x+1, how do you find an equation of the tangent line that has slope 2?

Answer 1

get the derivative
make the derivative equal to 2 and solve for x

Answer 2

You mean, take 4x-2 and make it 4x=2 and x=2?

Answer 3

Or 4x-2=2?

Answer 4

\[\frac{d}{dx}2x^2 - 2x + 1\]\[\frac{d}{dx}=4x -2\]\[4(2) -2 = ?\]

Answer 5

6

Answer 6

But now what?

Answer 7

Use point slope form to find y1

Answer 8

I don't have any points to plug into point slope form or am I missing something?

Answer 9

you're missing something

Answer 10

I have slope 2 and whatever 6 is after I put 2 in for x . Now I'm lost

Answer 11

The 6 is the X coordinate that we're dealing with

Answer 12

Well, I can get to y-ysub1=2x-12 with what I have but then how do I find ysub1?

Answer 13

Use an initial condition to find the Y intercept

Answer 14

I don't understand what that means, I've never heard of an initial condition.

Answer 15

say we have f(x) = x+2+c
and we have initial condition that f(3) =2
we can use this to solve for c
2=3+2+c
c=-3

Answer 16

an initial condition is just a given point

Answer 17

OK, that makes sense, the only given point was slope 2 though

Answer 18

So I still don't understand how to find it.

Answer 19

are you sure you were not given more? tangent lines are at a point.

Answer 20

This is the question here: For the curve f(x)=2x^2-2x+1, find an equation of the tangent line that has slope 2?

Answer 21

That's the only information given.

Answer 22

4x-2=2
so x = 1
only one spot on the curve has a derivative of 2
and thus only one line
so
we know the derivative at x=1 is 2
so plug 1 in for x in the original equation
and you get 1
so your point is (1,1)

Answer 23

y=2x+b with point (1,1)
1=2+b so b=-1
so
your equation is y=2x-1
this is the tangent line, to your curve at the point (1,1)

Answer 24

and is the only tangent line to your curve with slope 2

Answer 25

understand?

Answer 26

I'm going through it in my head step by step. So, I don't need the x=6 or the ysub1 to find this equation then?

Answer 27

I don't know why @hobbs987 wrote 4(2)-2=?
f'(x) has slope as its range, the domain is still "position"

Answer 28

so f'(2) makes no since in this context.

Answer 29

OK, I think I've got it now. Thanks for your help!

Answer 30

np

Answer 31

the key to this, is your function only has 2 as its derivative at one spot, namely (1,1).
if it had more than one place where its derivative was 2, then we would have more than one possible tangent line, and thus the answer would just be y=2x+b. But with only one spot (1,1) we can say for sure that b=-3

Answer 32

Wait, why is b=-3?

Answer 33

typo b=-1

Answer 34

OK and when you say that it only has 2 as its derivative, your talking about slope 2 right?