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anonymous

  • 5 years ago

Tangent line equation. (a, f(a)), f(x) = x^2, with a = 2.

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  1. anonymous
    • 5 years ago
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    there are 2 ways to solve this problem

  2. anonymous
    • 5 years ago
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    ok!

  3. anonymous
    • 5 years ago
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    1) By using the definition and I forgot abt the other way lol

  4. anonymous
    • 5 years ago
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    hahaha , ok, lets use the definition

  5. anonymous
    • 5 years ago
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    first : (a, f(a) ) is going to be : (2, 4)<-- you'll use these points later to find the equation we'll have to find the slope first

  6. anonymous
    • 5 years ago
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    >_< calculus I lol, alright, remind me, m = limit of that function

  7. anonymous
    • 5 years ago
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    f(x) - f(a) = f'(a) . (x - a)

  8. anonymous
    • 5 years ago
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    LOL! that's it! find the derivative!

  9. anonymous
    • 5 years ago
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    you have f(a) = 4, and a = 2

  10. anonymous
    • 5 years ago
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    are you sure that you have to find the derivative? I remember something with limits

  11. anonymous
    • 5 years ago
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    \[\ m= lim_{h \rightarrow 0}f(a) - f(a+1)/h\] that's the equation needed if we want to find the slope using the definition , right?

  12. anonymous
    • 5 years ago
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    yeap!

  13. anonymous
    • 5 years ago
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    alright! all we have to do is plug in the values we have

  14. anonymous
    • 5 years ago
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    hmmm if f(x) = x^2, then f(a) = a^2 , right?

  15. anonymous
    • 5 years ago
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    that's correct.

  16. anonymous
    • 5 years ago
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    then,\[= \lim_{h \rightarrow 0} (a^2 -a^2-1)/h\] = -1/h...hmm there's something wrong. h must be canceled

  17. anonymous
    • 5 years ago
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    LOL! no no no wait!

  18. anonymous
    • 5 years ago
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    \[\lim_{h \rightarrow 0} f(a) - f(a+h)/h \] that's the right equation LOL! sorry ^^"

  19. anonymous
    • 5 years ago
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    np

  20. anonymous
    • 5 years ago
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    so you'll get:\[=\lim_{h \rightarrow 0} (a^2 -a^2 -h)/h\]\[=\lim_{h \rightarrow 0} -h/h\] m = -1 ^_^ there we have found m and we have the points (2,4) <-- you know how I got them right?

  21. anonymous
    • 5 years ago
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    a = 2, f(a) = (2)^2 = 4 (2,4)

  22. anonymous
    • 5 years ago
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    ahhhh

  23. anonymous
    • 5 years ago
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    i got it. thanks!

  24. anonymous
    • 5 years ago
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    soooooooooooo, we'll use the equation which is : y -yo = m (x-xo) y - 4 = = -1(x-2) ^_^ LOL np :)

  25. anonymous
    • 5 years ago
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    sorry abt the mess though >_<

  26. anonymous
    • 5 years ago
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    np :)

  27. anonymous
    • 5 years ago
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    ^_^ good luck

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