Question

The minimum value of the expression $x^2-8x+17$ is

• A. $-1$
• B. $-2$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

$f\left(x\right)=x^2-8x+17$
Differentiating the above function with respect to x.
$f^{\prime }\left(x\right)=2x-8$
$=0$
Or
$2x-8=0$
$x=4$.
Now
$f"\left(x\right)=2$
or
$f"(x{)}_{x=4}>0$
Hence the function attains a minimum value at x equal to 4.
Therefore
$f\left(4\right)=16-32+17$
$=-16+17$
$=1$.