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MioMath 2024 Paper 2 · Q10

Paper 2Logic & proofFunctions & graphs

For a cubic function ax3+bx2+cx+dax^3+bx^2+cx+d, there are two local extrema, one at x>0x>0 and the other at x<0x<0. What is the necessary and sufficient condition for this to occur?

Ab>3ab>3a
Bb<3ab<3a
Cac>0ac>0
Dac<0ac<0
Eb2>3acb^2>3ac
Fb2>4acb^2>4ac

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