Function f(x) = |x| - |x-1| is monotonically increasing when (1) x < 0 (2) x > 1 (3) x < 1 (4) 0 < x < 1

Question:

Function f(x) = |x| - |x-1| is monotonically increasing when 

(1) x < 0 

(2) x > 1 

(3) x < 1 

(4) 0 < x < 1

Answer: option (4) "0<x<1"

Explanation:

Given: f(x)=|x| - |x-1| 

To find: At which condition f(x) is Monotonically increasing. 

Solution: 

f(x)=|x| - |x-1| 

for x>1 

f(x)=x-(x-1)=1 

f '(x)=0 

for 0<x<1 

f(x)=x-(1-x)=2x-1

 f(x)=2>0 

Monotonically increasing 

for x<0 

f (x)=-x-(1-x)= -1 

f '(x)=0 

0<x<1 is the interval for f(x) to be monotonically increases. 

Hence, option (4) "0<x<1" is the correct answer.