Question

find unit vectors parallel to tangent line to curve y=x^2 at point (2,4)

Answer 1

Can you find f'(x) ?

Answer 2

-> m = f'(2)

Answer 3

@dizliz24 Hello...oo

Answer 4

Sorry, I was working on the problem. I am completely lost on this one. I have no idea where to start

Answer 5

I forget how to do derivatives

Answer 6

f(x) = x^n --> f'(x) = nx ^(n-1)
Now do you remember and start?

Answer 7

Aha, yes. But how do I relate this to the information that I have available

Answer 8

f(x) = x^n = x²
Does it look related now?

Answer 9

Yes, so I have 2x=4, correct? What should be my next step

Answer 10

Do you understand what's 4?

Answer 11

I am in a toss up. I am not sure if it is y or if it is 2x such that x=2 which is also 4

Answer 12

Did you read my second post?

Answer 13

yes. what is m

Answer 14

y = mx + b
What's m?

Answer 15

I know that has something to do with slope

Answer 16

Yes, slope! m is slope!

Answer 17

Okay, m is the slope. So why does m=f'(2)

Answer 18

That's how you find slope :)

Answer 19

That's news to me. Now, what do I do with the slope

Answer 20

So that's the basic you should memorize!

Answer 21

Then what do you know about unit vector?

Answer 22

Oh a unit vector is a vector whose length is 1

Answer 23

How to find magnitude of vector?

Answer 24

Thats one I am not sure of

Answer 25

Do you know distance formula?

Answer 26

d=sqrt((x2-x1)+(y2-y1)

Answer 27

You miss the square sign (x2-x1)² + ( )²
Great, distance formula to calculate magnitude of vector :)

Answer 28

Yes, I did.

Answer 29

How do I use this formula

Answer 30

Since the unit vector parallel to m = 4 => it's coordinate < 1, 4>
and it's magnitude √1 + 16 = √17
Thus the unit vector is < 1/√17, 4/√17 >

Answer 31

Okay but why do we use 1, because it is a unit vector?

Answer 32

When you divide for magnitude => Unit vector!

Answer 33

what do you divide

Answer 34

I don't understand what we are dividing and why we divide

Answer 35

Then you need to look at your note, notebook about unit vector!

Answer 36

I see what you mean. I feel stupid. thank you for your help:)