Q7 of 64 Page 10

Show that the function F(x) = is

Neither continuous and nor differentiable, if m≤0.

LHL =


=


=


= Not defined, as m 0


RHL =


=


=


= Not Defined, as


Since, LHL and RHL are not Defined ,So f(x) is not continuous.


Let x = 0 for


Now,


(LHD at x = 0) =


=


=


=


=


=


= Not Defined , as


(RHD at x = 0) =


=


=


=


= Not Defined , as


Hence, f(x) is not differentiable at x = 0 for


More from this chapter

All 64 →
7

Show that the function F(x) = is

Differentiable at x = 0, if m > 1.

 7

Show that the function F(x) = is

Continuous but not differentiable at x = 0, if 0<m<1.

 8

Find the values of a and b so that the function

f(x) =


is differentiable at each x € R.

 9

Show that the function

F(x) =


Is continuous but not differentiable at x = 1.