Question

Can we differentitate mod x

Answer 1

definitely yes, but the derivative function won't be defined at x=0

Answer 2

\[\large |x| = \begin{cases} -x : x\le 0 \\ ~~x : x\gt 0 \end{cases}\]

Answer 3

how do we do it ?

Answer 4

\[\large |x|' = \begin{cases} -1 : x\lt 0 \\ ~~1 : x\gt 0 \end{cases} \]

Answer 5

Notice that we cannot define the derivative at x=0 because the function is not smooth. if you use the limit definition of derivative, you will get DNE at x=0 :

Answer 6

Ok,
Suppose i want to find maxima of this function then
\[\huge \left| 2x-4 \right|+\left| x+5 \right|\]

Answer 7

Can we do that ? by differentitation

Answer 8

I think it would become zero because the denominator would turn zero , and thus it would be undefined

Answer 9

what about function at -1 it has a maximum value of 10

Answer 10

@ganeshie8

Answer 11

once we figured out the derivative, we an use it everywhere

Answer 12

what do we know about relation between derivative and extrema of a function ?