Show that decreases in the interval [0, ∞) and increases in the interval (-∞, 0].

Question

Philoid · Accepted Answer

We have,

Case 1

When x [0,)

Let , (0,] and

⇒

⇒ f(x₁)< f(x₂)

f(x) is decreasing on[0,∞).

Case 2

When x (-,0]

Let >

⇒

f(x) is increasing on(-∞,0].

Thus, f(x) is neither increasing nor decreasing on R.