Question

Limits,

Can you help me find out this specific thing I dont know how to find out http://screencast.com/t/PUvesX4N

Answer 1

Once you find f'(x), plug in a to get the slope of the line, m.

Then you want to get it in the form y=mx+b, by using the fact it passes through the point (a, f(a))

Answer 2

Do you know how to take the derivative?
If so, then first take the derivative of the function, then evaluate it at the given a -- this is "m", the slope of the tangent line.
Now, evaluate the function at the given a. This we'll call "y1"
The tangent line is:
y-y1 = m (x-a)

Answer 3

Can please someone tell me what is a slope just so I get the bigger picture of whats going on?

Answer 4

Slope is the steepness of the line, or rate of change. Remember back in algebra, equations y=mx+b have a slope of m.

Answer 5

@BTaylor what do you mean by "Now, evaluate the function at the given a. " ?

Answer 6

so, for number 9, f(x) = 2x^2. The given "a" is 1. So evaluating the function at a means you plug in a for x, and get 2(1)^2, which is 2.

Answer 7

That means plug in x=1 (since a=1) into f = 2x^2

Answer 8

@agent0smith is right.
To visualize this tangent line, click this link:
http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=tangent%20line%20to%202x%5E2%20at%20x%3D1

Answer 9

I got y1 = 0

Answer 10

y1 = -2

Answer 11

y1 = 2 :D **

Answer 12

the last one is right. y1 = 2.

Answer 13

so that's the answer?? y1 = 2 and I am done? Nothing else needed?

Answer 14

No... did you find the slope?

Answer 15

its 4

Answer 16

yes. because the derivative is 4x, evaluated at x=1 gives you 4(1) =4

Answer 17

So then put it in point-slope form:
y-y1 = m (x-x1)

where x1 = 1, y1= 2

Answer 18

yea

Answer 19

I did all that and I got y1 = 2 in the end, I am done ?

Answer 20

Wait, no, where is your x going?

y-y1 = m (x-a)

y - 2 = 4(x-1)

Answer 21

x-1 = 0

Answer 22

x = 1

Answer 23

x is x.

Answer 24

a is 1.

Answer 25

then why y is not y too and had to be replaced

Answer 26

y is y.

y-2 = 4 (x-1)

Answer 27

You're using point slope form to write the equation of a line: http://www.purplemath.com/modules/strtlneq2.htm

Answer 28

Nice! I see now! Thank you both! I wish I could give more medals!

Answer 29

Your line has a slope of m=4, and passes through the point (1, 2) then you just plug it into the point slope formula.

Answer 30

oh i see

Answer 31

And again, this is what you have found: http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=tangent%20line%20to%202x%5E2%20at%20x%3D1

Answer 32

yes