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onegirl Group Title

Find the linear approximation to f(x) at x = x o. Graph the function and its linear approximation. f(x) = sin 3x, x 0, = 0

  • one year ago
  • one year ago

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  1. onegirl Group Title
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    @satellite73 can u help please?

    • one year ago
  2. satellite73 Group Title
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    this is the same as "find the equation of the line tangent to the graph of \(y=\sin(3x)\) at \((0,0)\)"

    • one year ago
  3. satellite73 Group Title
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    take the derivative, replace \(x\) by 0 for the slope (you will get 3) and then use the point slope formula

    • one year ago
  4. satellite73 Group Title
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    since the point is \((0,0)\) the equation of the line will be \(y=3x\)

    • one year ago
  5. onegirl Group Title
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    ok so find the derivative of sin 3x right?

    • one year ago
  6. satellite73 Group Title
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    yes

    • one year ago
  7. onegirl Group Title
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    Ok so i got 3cos(3x)

    • one year ago
  8. satellite73 Group Title
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    yes now evaluate at \(x=0\) to find your slope

    • one year ago
  9. onegirl Group Title
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    ok i got 3

    • one year ago
  10. satellite73 Group Title
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    yes

    • one year ago
  11. satellite73 Group Title
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    that is the slope of your line

    • one year ago
  12. onegirl Group Title
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    okay so now i have to use the point slop formula?

    • one year ago
  13. satellite73 Group Title
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    yes

    • one year ago
  14. satellite73 Group Title
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    but the point is \((0,0)\) so it is just \(y=3x\)

    • one year ago
  15. onegirl Group Title
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    okay so what do i do next?

    • one year ago
  16. satellite73 Group Title
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    you are done

    • one year ago
  17. onegirl Group Title
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    okay

    • one year ago
  18. electrokid Group Title
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    linear approximation of f(x) at x=x0: \[f(x)=f(x_0)+(x-x_0)f'(x_0)\]

    • one year ago
  19. electrokid Group Title
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    you can use this way too. (notice the resemblance to equation of line)

    • one year ago
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