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anonymous

  • 4 years ago

Let f(x)=x^2+x+14. What is the value of x for which the tangent line to the graph of y=f(x) is parallel to the x-axis?

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  1. anonymous
    • 4 years ago
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    the answer is NOT -1

  2. Xishem
    • 4 years ago
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    First, take the derivative of the function.

  3. anonymous
    • 4 years ago
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    o i messed that up. now im getting -1/2 but its still wrong.

  4. Xishem
    • 4 years ago
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    First, what is the derivative of the function? I will guide you through the problem.

  5. anonymous
    • 4 years ago
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    2x+1

  6. Xishem
    • 4 years ago
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    Ok. So \[f'(x)=2x+1\]Now, this function represents the slope of the tangent line at any given value of x. What slope does a line have to have to be parallel to the x-axis?

  7. anonymous
    • 4 years ago
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    zero like you said earlier

  8. Xishem
    • 4 years ago
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    Alright, so when the slope of the tangent line is 0, that is when the tangent line is parallel to the x-axis. The derivative of f(x) represents the slope of the tangent line. Therefore, set the f'(x) equal to 0, and then solve for x, and that will give you the answer of \[\frac{-1}{2}\]That is the correct answer, so I'm not sure why it appears as wrong. Make sure you copied down the problem correctly, I suppose.

  9. anonymous
    • 4 years ago
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    o it should be "what is the value of f(x)" not "x"

  10. Xishem
    • 4 years ago
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    The wording of that question seems strange. I think it means this: \[f(\frac{-1}{2})=(\frac{-1}{2})^2+\frac{-1}{2}+14=13.75\]Which is the value of f(x) given a value of x where the tangent line is parallel to the x-axis.

  11. anonymous
    • 4 years ago
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    yeah, that correct

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