## Christos 2 years ago Limits, Can you help me find out this specific thing I dont know how to find out http://screencast.com/t/PUvesX4N

1. agent0smith

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))

2. BTaylor

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)

3. Christos

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

4. agent0smith

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

5. Christos

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

6. BTaylor

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.

7. agent0smith

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

8. BTaylor

@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

9. Christos

I got y1 = 0

10. Christos

y1 = -2

11. Christos

y1 = 2 :D **

12. BTaylor

the last one is right. y1 = 2.

13. Christos

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

14. agent0smith

No... did you find the slope?

15. Christos

its 4

16. BTaylor

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

17. agent0smith

So then put it in point-slope form: y-y1 = m (x-x1) where x1 = 1, y1= 2

18. Christos

yea

19. Christos

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

20. agent0smith

Wait, no, where is your x going? y-y1 = m (x-a) y - 2 = 4(x-1)

21. Christos

x-1 = 0

22. Christos

x = 1

23. agent0smith

x is x.

24. agent0smith

a is 1.

25. Christos

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

26. agent0smith

y is y. y-2 = 4 (x-1)

27. agent0smith

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

28. Christos

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

29. agent0smith

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.

30. Christos

oh i see

31. agent0smith

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

32. Christos

yes