Question

The minimum value of $f\left(x\right)=x^2+2x+3,x\in R$ is equal to

• A. $2$
• B. $3$
• C. $4$
• D. $1$

Answer 1

The correct option is A $2$

$f\left(x\right)=x^2+2x+3$

For minima:

$f^{\prime }\left(x\right)=0$

$f^{\prime }\left(x\right)=2x+2=0$

$⟹x=-1$

Hence minimum value of $f\left(x\right)$ is at $x=-1$, i.e.

$f(-1)=(-1{)}^2-2+3=2$