A) \[f(x)\]is strictly increasing function
B) \[f(x)\]has a local maxima
C) \[f(x)\]strictly decreasing function
D) \[f(x)\]is bounded
Correct Answer: A
Solution :
Given, \[f(x)={{x}^{3}}+b{{x}^{2}}+cx+d\] \[\Rightarrow \] \[f(x)=3{{x}^{2}}+2bx+c\] (As we know, if\[a{{x}^{2}}+bx+c>0\]for all\[x\Rightarrow a>0\]and\[D<0\]) Now, \[D=4{{b}^{2}}-12c=4({{b}^{2}}-c)-8c\] (where\[{{b}^{2}}-c<0\]and\[c>0\]) \[\therefore \] \[D=(-ve)ie,\,\,D<0\] \[\Rightarrow \] \[f(x)=3{{x}^{2}}+2bx+c>0\] for all\[x\in (-\infty ,\,\,\infty )\]. (as\[D<0\]and\[a>0\]) Hence,\[f(x)\]is strictly increasing function.
You need to login to perform this action.
You will be redirected in
3 sec
