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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 xaxis?
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 xaxis?

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Xishem
 4 years ago
Best ResponseYou've already chosen the best response.1First, take the derivative of the function.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0o i messed that up. now im getting 1/2 but its still wrong.

Xishem
 4 years ago
Best ResponseYou've already chosen the best response.1First, what is the derivative of the function? I will guide you through the problem.

Xishem
 4 years ago
Best ResponseYou've already chosen the best response.1Ok. 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 xaxis?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0zero like you said earlier

Xishem
 4 years ago
Best ResponseYou've already chosen the best response.1Alright, so when the slope of the tangent line is 0, that is when the tangent line is parallel to the xaxis. 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
 4 years ago
Best ResponseYou've already chosen the best response.0o it should be "what is the value of f(x)" not "x"

Xishem
 4 years ago
Best ResponseYou've already chosen the best response.1The 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 xaxis.
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