Question

$f\left(x\right)$ attains maximum value when $x$ equals

• A. $0$
• B. $-2$
• C. $2$
• D. $1$

Answer 1

The correct option is A $0$

$f\left(x\right)=3x^4+4x^3-12x^2+a$.
$\Rightarrow f^{\prime }\left(x\right)=12x^3+12x^2-24x$
$=12x(X^2+x-2)=12x(x+2)(x-1)$


Clearly $f^{\prime }\left(x\right)$ changes its sign from $+ve$ to $-ve$ in the neighbourhood of $0$, hence $f\left(x\right)$ attains maximum value at $x=0$.
$f^{\prime }\left(x\right)$ changes its sign from $-ve$ to $+ve$ in the neighbourhood of $x=1$ & $x=-2$.