Question

The smallest value of $x^2-3x+3$ in the interval $(-3,\frac{3}{2})$ is

• A. $\frac{3}{4}$
• B. 5
• C. -15
• D. -20

Answer 1

The correct option is A $\frac{3}{4}$

$f^{\prime }\left(x\right)=2x-3$
$f^{\prime }\left(x\right)=0$ when $x=\frac{3}{2}$
$f^{\prime }\left(x\right)>0$ when $x>\frac{3}{2}$
$f^{\prime }\left(x\right)<0$ when $x<\frac{3}{2}$
$f\left(x\right)$ is minima at $x=\frac{3}{2}$
$f\left(\frac{3}{2}\right)=\frac{3}{4}$