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  4. For f(x)=x3+bx2+cx+d, if b2>4c>0 and b,c,d∈ R, then f(x)

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Q. For $f\left(x\right)=x^{3}+bx^{2}+cx+d,$ if $b^{2}>4c>0$ and $b,c,d\in R,$ then $f\left(x\right)$

NTA AbhyasNTA Abhyas 2020Application of Derivatives

Solution:

$f^{'} \left(x\right) = 3 x^{2} + 2 b x + c$
Discriminant $=4\left(b^{2} - 3 c\right)>4c>0$ (as $c > 0$)
Hence, $f\left(x\right)$ has a local maxima and a local minima