Without using the derivative, show that the function f(x) = | x | is A. strictly increasing in (0, ∞) B. strictly decreasing in (-∞, 0).

Question

Philoid · Accepted Answer

We have,

f(x) = |x| =

(a)Let , (0,) and

⇒

So, f(x) is increasing in (0,)

(b) Let , (-∞, 0)and

⇒

f(x) is strictly decreasing on(-∞, 0).