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MioMath 2024 Paper 2 · Q11

Paper 2Functions & graphsAlgebra

Given the function f(x)=x3+px2+qf(x)=x^3+px^2+q, it has a local maximum at x=0x=0 and 3 distinct roots. Find the conditions for pp and qq.

A827p3<q<0\dfrac{8}{27}p^3<q<0
B0<q<−827p30<q<-\dfrac{8}{27}p^3
C427p3<q<0\dfrac{4}{27}p^3<q<0
D0<q<−427p30<q<-\dfrac{4}{27}p^3

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