TMUAmockz Set 1 Paper 2 · Question 14

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TMUAmockz Set 1 Paper 2 · Q14

Paper 2Functions & graphsAlgebra

The function $f(x)=x^3+ax^2-a^2x+b$ has a local maximum at $x=a/3$ and three distinct real roots. What conditions must $a$ and $b$ satisfy?

a<0

and

-\dfrac{5a^3}{27}<b<-a^3

a>0

and

\dfrac{5a^3}{27}<b<-a^3

a<0

and

-a^3<b<\dfrac{5a^3}{27}

a<0

and

\dfrac{5a^3}{27}<b<-a^3

a<0

and

\dfrac{4a^3}{27}<b<-a^3

a<0

and

\dfrac{5a^3}{27}<b<a^3

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