Let f(x)=ax^3+bx^2+cx+d , find conditions for a,b.c and d so that a) f has no horizontal tangent line. b) f has aunique horizontal tangent line. c) f has tow horizontal tangent lines
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Originally Posted by BAHADEEN Let f(x)=ax^3+bx^2+cx+d , find conditions for a,b.c and d so that a) f has no horizontal tangent line. b) f has aunique horizontal tangent line. c) f has tow horizontal tangent lines If you take the derivative you get So a graph has a horizontal tangent when the derivative is equal to zero. so we need to analyze the discriminant of the quadratic. Can you finish from here?
Originally Posted by TheEmptySet If you take the derivative you get So a graph has a horizontal tangent when the derivative is equal to zero. so we need to analyze the discriminant of the quadratic. Can you finish from here? How could I find the three conditions? thank you for help
Originally Posted by BAHADEEN How could I find the three conditions? thank you for help The discrimiant is This will have no solutions when the discrimiant is negative. This will have exactly one solution when the discrimiant is equal to zero. This will have two solutions when the discrimiant is positive.
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