SOLUTION: Determine the k values such that y= 4x + k does not intersect the parbola y=-3x^2 -x +4

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Question 291563: Determine the k values such that y= 4x + k does not intersect the parbola y=-3x^2 -x +4
Answer by solver91311(24713) About Me  (Show Source):
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Take the first derivative of your parabola function.



The slope of the line is 4, so set the derivative function equal to that slope:





If the line were actually tangent, then the point of tangency would be:



Do the arithmetic:



So, for a tangent line:



Hence,



So, if the line must not intersect the parabola: