If x is real, then the minimum value of x 2 - 8 x + 1 7 is:

Question

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

Smart Achievers · Accepted Answer

(3)

Ans. 1

Explanation:

Let $f (x) = x^{2} - 8 x + 17$

$∴$ $f' (x) = 2 x - 8$

So, $f' (x) = 0,$ gives $x = 4$

Now, $f'' (x) = 2 > 0,$ $\forall x$

So, $x = 4$ is the point of local minimum.

Hence, the minimum value of $f (x)$ = at $x = 4$ .

$f (4) = 4^{2} - 8 (4) + 17 = 16 - 32 + 17 = 1$

$∴$ Minimum value = 1

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