Question

If x is real, the minimum value x² - 8x + 17 is
(a) -1 (b) 0 (c) 1 (d) 2

Answer 1

Let f(x) = x² − 8x + 17

Differentiating both sides with respect to x, we get

$f\text{'}\left(x\right)=2x-8$

For maxima or minima,

$f\text{'}\left(x\right)=0$

$\Rightarrow 2x-8=0$

$\Rightarrow x=4$

Now,

$f\text{'}\text{'}\left(x\right)=2>0$

So, x = 4 is the point of local minimum of f(x).

∴ Minimum value of f(x) = f(4) = (4)² − 8 × 4 + 17 = 16 − 32 + 17 = 1

Thus, the minimum value of x² − 8x + 17 is 1.

Hence, the correct answer is option (c).