If x is real, the minimum value of x^2 - 8x + 17 is: - Vidyadip

MCQ

If $x$ is real$,$ the minimum value of $x^2 - 8x + 17$ is:

A
$-1$
B
$0$
✓
$1$
D
$2$

✓

Answer

Correct option: C.

$1$

Let $f(x) = x^2 - 8x + 17$
$\therefore f'(x) = 2x - 8$
So$, f'(x) = 0$, gives $x = 4$
Now $,f''(x) = 2 > 0$, $\forall x$
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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