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ZeroAT

  • 3 years ago

Write an equation for the tangent line to f(x) = -4x + 3/x at x = -1 How do i solve this?

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  1. LolWolf
    • 3 years ago
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    So, we need to know the slope at this point, this is given by: \[ \frac{d}{dx}\left(-4x+\frac{3}{x}\right)=-4-\frac{3}{x^2} \]Evaluating this at \(x=-1\): \[ -4-\frac{3}{x^2}\Bigg|_{x=-1}=-4+3=-1 \]So the slope of the line is -1 at this point. Now, find a point on the line: \[ -4(-1)+\frac{3}{-1}=-7=y \]Which means: \[ y+7=-1(x+1) \]Et voilá.

  2. ZeroAT
    • 3 years ago
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    thank you.

  3. ZeroAT
    • 3 years ago
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    Which would be the correct answer: A) -7x + y = -6 B) -6x + 2y = -5 C) 7x + y = -6 D) 6x + 2y = -5

  4. LolWolf
    • 3 years ago
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    Wait, I screwed up, it's: \[ -4-\frac{3}{x^2}\Bigg|_{x=-1}=-4-3=-7 \]So: \[ y+7=-7(x+1) \]

  5. ZeroAT
    • 3 years ago
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    oh! that explains why i coudnt get the answer. Thanks for the assistance

  6. LolWolf
    • 3 years ago
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    Sure thing

  7. ZeroAT
    • 3 years ago
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    One more question..How would i get the end results in one of those 4 possible results i mentioned? can you show me?

  8. LolWolf
    • 3 years ago
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    Just solve for the same form, it's roughly the same case.

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