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anonymous

  • 4 years ago

Let f(x) = 3 x^2 - 8. Find an equation of the line tangent to the graph of f at the point where x = -3. y =

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  1. Mertsj
    • 4 years ago
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    Do you know that the first derivative is the tangent function?

  2. anonymous
    • 4 years ago
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    the power rule?

  3. Mertsj
    • 4 years ago
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    Yes

  4. anonymous
    • 4 years ago
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    f'(X)= rx^r-1

  5. Mertsj
    • 4 years ago
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    f'(x)=6x

  6. anonymous
    • 4 years ago
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    that the deriv 6x so plug that in the equation

  7. Mertsj
    • 4 years ago
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    At x = -3, f'(x)=-18 and that is the slope of the tangent at x = -3

  8. anonymous
    • 4 years ago
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    y=mx+b right? or y-y1=mx-x1

  9. Mertsj
    • 4 years ago
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    y=6x That is the equation of the tangent function. At x = -3, it has a value of -18 and that is the slope of the tangent at that point.

  10. Mertsj
    • 4 years ago
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    Why don't you draw the graph of the parabola and then draw the tangent at x = -3 and see what it looks like?

  11. Mertsj
    • 4 years ago
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    That would help you understand.

  12. anonymous
    • 4 years ago
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    wait what is the full equation y=6x?

  13. Mertsj
    • 4 years ago
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    So if you want the equation of the tangent you know its slope is -18 and you know it goes through the point (-3,19) So use either y= mx+b or point slope form. Whichever you prefer.

  14. Mertsj
    • 4 years ago
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    y=6x is the function that gives you the slope of the tangent at any x value of the parabola.

  15. anonymous
    • 4 years ago
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    y=-18(-3)+b

  16. Mertsj
    • 4 years ago
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    \[y-19=-18(x+3)\] \[y=-18x-35\]

  17. Mertsj
    • 4 years ago
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    y=-18(-3)+b 19=-18(-3)+b

  18. anonymous
    • 4 years ago
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    for some reason im not writing it corrrectly bcause my book says its wrong

  19. Mertsj
    • 4 years ago
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    what does your book say it is?

  20. anonymous
    • 4 years ago
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    equation of the tangent line of y = x3 at x = 2

  21. anonymous
    • 4 years ago
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    3 x^2 = f(x)+8

  22. Mertsj
    • 4 years ago
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    We are not working with the function y = x^3. We are doing y = 3x^2-8

  23. Mertsj
    • 4 years ago
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    What does your book say for this one?

  24. anonymous
    • 4 years ago
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    it says y=-18x+b

  25. Mertsj
    • 4 years ago
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    For the final answer?

  26. anonymous
    • 4 years ago
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    yeah they only want the equation

  27. anonymous
    • 4 years ago
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    of a line

  28. Mertsj
    • 4 years ago
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    Well it would be easy to find b and if i were you I would give both answers.

  29. anonymous
    • 4 years ago
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    ok thanks

  30. Mertsj
    • 4 years ago
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    Because the problem specifies to find the equation of the tangent at x = -3.

  31. Mertsj
    • 4 years ago
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    yw

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