Question

Which one of the following is not true?

• A. $f(x)=x|x|$ is differentiable in $(-1,1)$
• B. $g(x)=\sqrt{|x|}$ is differentiable in $(4,5)$
• C. $h(x)=|x-2|+|x+3|$ is differentiable in $(3,2)$
• D. $k(x)=|x+1|+|x-6|$ is differentiable in $(-1,6)$
• E. $t(x)=x+[x]$, where $[x]$ is greatest integer function, is differentiable at $x=0$

Hint:

Differentiability requires continuity first—check for jumps or corners.

Answer 1

Answer: (E)