Choose the correct answer from the given four options : If x is r…

MCQ

Choose the correct answer from the given four options : If $x$ is real, the minimum value of $x^2-8 x+17$ is :

A
$-1$
B
$0$
✓
$1$
D
$2$

✓

Answer

Correct option: C.

$1$

Let $f(x)=x^2-8 x+17$
$\therefore f^{\prime}(x)=2 x-8$
So, $f^{\prime}(x)=0$, gives $x=4$
Now, $f ^{\prime \prime}( x )=2 > 0, \forall x$
So, $x=4$ is the point of local minima.
$\therefore$ Minimum value of $f ( x )$ at $x =4$,
$f(4)=4 \times 4-8 \times 4+17=1$

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