The value of $x$, for which the function $f(x)=x(x-2)$ attains its minimum value, is:
Answer & explanation
Correct answer: option 2
$f(x) =x(x-2)$
$=x^2-2 x$
so $f'(x)=2 x-2$
differential w.r.t x
finding critical points as f'(x) = 0
⇒ 2x - 2 = 0
⇒ x = 1
f''(x) = 2
differentiating f'(x) w.r.t x
for f''(1) = 2 > 0
⇒ 1 is point of minima