Question

Minimum value of the expression $x^2-2x+3\text{for}x\in [2,5)$ is equal to -

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is C $3$

REF.Image

$f\left(x\right)=x^2-2x+3$, $x\in [2,5)$

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

$\Rightarrow x=1$

minima at x=1

$\Rightarrow$ for $x\in [2,5),f\left(x\right)$ is

minimum at x=2

$\Rightarrow f\left(2\right)=2^2-2\times 2+3$

$=3$