Question

The function $f(x)=2x^3-3x^2-12x+4$, has

• A. two points of local maximum
• B. two points of local minimum
• C. one maxima and one minima
• D. no maxima or minima

Answer 1

Answer: (C)

$f(x)=2x^3-3x^2-12x+4$
$\Rightarrow f^{\prime }(x)=6x^2-6x-12$
$=6(x^2-x-2)$
For maxima and minima, $f^{\prime }(x)=0$
$\therefore 6(x-2)(x+1)=0$
$\Rightarrow x=2$, $-1$
Now, $f^{\prime \prime }(x)=12x-6$
At $x=2$
$f^{\prime \prime }(x)=24-6=18>0$
$\therefore x=2$, local min. point
At $x=-1$
$f^{\prime \prime }(x)=12(-1)-6=-18<0$
$\therefore x=-1$ local max. point