Question:
Mark the correct alternative in the following:
Function $f(x)=|x|-|x-1|$ is monotonically increasing when
A. $x<0$
B. $x>1$
C. $x<1$
D. $0
Solution:
Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on $(a, b)$ is that $f^{\prime}(x)>0$ for $a l l ~ x \in(a, b)$
Given:-
For $x<0$
$f(x)=-1$
for $0 $f(x)=2 x-1$ for $x>1$ $f(x)=1$ Hence $f(x)$ will increasing in $0