Question

The minimum value of the function $f\left(x\right)=9x^2+12x+2$ is

• A. $4$
• B. $-4$
• C. $2$
• D. $-2$

Answer 1

The correct option is D $-2$

$f\left(x\right)=9x^2+12x+2\Rightarrow f^{\prime }\left(x\right)=18x+12=0\Rightarrow x=-\frac{2}{3}$
$f^{\prime \prime }\left(x\right)=18>0$
So $x=-\frac{2}{3}$ will give minima of the function.
$f(-\frac{2}{3})=9\times \frac{4}{9}-12\times \frac{2}{3}+2=-2$