Question

The conditions for y=ax⁴+bx³+cx²+dx+e to have points of inflection is

A)b²-4ac>0 B)3b²-8ac=0

^{C)3b2 -8ac>0} D) 3b²-8ac<0

Answer 1

1. We must find the critical points where y” =0 or NOT DEFINED.
2. y'= 4ax³ +3bx² +2cx +d and. y''= 12ax² +6bx +2c
3. y'' is always defined that means for point of inflection, y'' must be zero for some real value, so for real solution D≥0.
4. D= 36b²-96ac≥0.

That is 3b²≥8ac.
OPTION C