Thank you for reporting, we will resolve it shortly
Q.
The condition that $f(x) = ax^3 + bx^2 + cx + d $ has no extreme value is
Application of Derivatives
Solution:
$f\left(x\right)=ax^{3}+bx^{2}+cx+d$.
$f'\left(x\right)=3ax^{2}+2bx+c$
For extreme values, $f'\left(x\right)=0$
$\therefore 3ax^{2}+2bx+c=0$
It has no roots if $4b^{2}-12\,ac < 0$
i.e., $b^{2} < 3a\,c$.