anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
the answer is NOT -1
Xishem
  • Xishem
First, take the derivative of the function.
anonymous
  • anonymous
o i messed that up. now im getting -1/2 but its still wrong.

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Xishem
  • Xishem
First, what is the derivative of the function? I will guide you through the problem.
anonymous
  • anonymous
2x+1
Xishem
  • Xishem
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?
anonymous
  • anonymous
zero like you said earlier
Xishem
  • Xishem
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.
anonymous
  • anonymous
o it should be "what is the value of f(x)" not "x"
Xishem
  • Xishem
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.
anonymous
  • anonymous
yeah, that correct

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