The graph of f(x)=2x^3+12x^2-126x+11 has two horizontal tangents. One occurs at a negative value of x and the other at a postive value of x. What is the negative value of x where a horizonal tangent occurs?
I know that you will need to take the derivative first of f(x) and that f'(x) = 6x^2+24x-126. But, I don't know how to find the positve and negative horizontal tangents.

Question

The graph of f(x)=2x^3+12x^2-126x+11 has two horizontal tangents. One occurs at a negative value of x and the other at a postive value of x. What is the negative value of x where a horizonal tangent occurs? 
I know that you will need to take the derivative first of f(x) and that f'(x) = 6x^2+24x-126. But, I don't know how to find the positve and negative horizontal tangents.

anonymous · Answer

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anonymous · Answer

those are they tangents, their slopes are the same as the slope of the function at those two points.  their slopes are zero.  the slope of the function is zero.