Question 1163296
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I suspect you mean <i><b>at which points on the graph of *[tex \Large f(x)\ =\ 2\ -\ 4^3] does the graph have a normal with a slope equal to 3?</b></i>


A normal to a curve is perpendicular to a tangent to the curve.  Perpendicular lines have negative reciprocal slopes.  So take the first derivative of your function and set that function equal to *[tex \Large -\frac{1}{3}].  Since you are dealing with a cubic polynomial, one would expect the derivative to be a quadratic with two zeros.
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
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