Locating Horizontal Tangent Lines

Question

Which of the following provides a correct example of the procedure for finding the x-values where a function's graph has horizontal tangent lines?

Accepted Answer

For $$f(x)=x^3-3*x+1$$, the derivative is $$f'(x)=3*x^2-3$$; setting this equal to zero gives $$3*x^2-3=0 \Rightarrow x^2=1\Rightarrow x=1 	ext{ or } x=-1$$, indicating horizontal tangent lines at these x-values.

Answer

For $$f(x)=x^3-3*x+1$$, setting the function equal to zero instead of its derivative leads to an incorrect identification of horizontal tangents.

Answer

Computing the derivative of $$f(x)=x^3-3*x+1$$ and finding values where it is nonzero does not help in locating horizontal tangent lines.

Answer

Using the second derivative of $$f(x)=x^3-3*x+1$$ rather than the first derivative is the proper method for finding horizontal tangents.

Locating Horizontal Tangent Lines

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