Question

The minimum value of $2x^3-9x^2+12x+4$ is

• A. 4
• B. 5
• C. 6
• D. 7
• E. 8

Answer 1

Answer: (E)

Let $y=2x^3-9x^2+12x+4$
On differentiating w.r.t. $x$, we get
$\frac{dy}{dx}=6x^2-18x+12$
$f^{\prime }(x)=0$
$\therefore 6x^2-18x+12=0$
$\Rightarrow x^2-3x+2=0$
$\Rightarrow (x-2)(x-1)=0$
$x=2$ or 1
Now, $\frac{d^{2}y}{d{x}^2}=12x-18>0$,
for $x=2$
$\therefore x=2$ is a point of local
$y_{\min }=16-36+24+4=8$