For which real numbers c is there a straight line that intersects the curve

y = x⁴ + 9x³ + cx² + 9x + 4

in four distinct points?

(In reply to A possible start by Kenny M)

I think merely an inflection point might work, as the straight line the curve is intersecting need not be horizontal. If the straight line goes through the inflection point and it's steep enough it will have four intersections with the curve.

Posted by Charlie on 2024-09-04 07:17:28