Question

For which value of x, the function $f(x) = x^{2} - 2x$ is

decreasing

• A. $x > 1$
• B. $x > 2$
• C. $x < 1$
• D. $x < 2$

Answer 1

Answer: (C)

$x < 1$

Answer 2

$f(x) = (x - 1)^{2} - 1$

Hence decreasing in$x < 1$

Alternative method: $f^{'}(x) = 2x - 2 = 2(x - 1)$

To be decreasing, $2(x - 1) < 0$ ⇒ $(x - 1) < 0$ ⇒ $x < 1$.