Question

f(x) = |x + 2| + |x – 1| is

(a) increasing in (– 1, ∞) 

(b) increasing in [– 1, ∞] 

(c) decreasing in (– ∞, – 2) 

(d) decreasing in [– ∞, – 2]

Answer 1

The correct option   (d) decreasing in [– ∞, – 2]

Explanation:

f(x) = |x + 2| + |x – 1| 

= – 2x – 1 for x < – 2 

= 3 for – 2 ≤ x ≤ 1

= 2x + 1 for x > 1 

∴ f'(x) = – 2 ------- x < – 2 

= doesn’t exist ---- x = – 2 

= 0 ------- – 2 < x < 1 

= doesn’t exist ----- x = 1 

= 2 ----- x > 1 

∴ f(x) is increasing in (1, ∞) and decreasing in (– ∞, – 2)