Q7 of 64 Page 10

Show that the function F(x) = is

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

LHL =


=


=


=


= 0 x k [when ]


= 0


RHL =


=


=


=


= 0 x k [when ]


= 0


LHL = RHL = f(0)


Since, f(x) is continuous at x = 0


For Differentiability at x = 0


(LHD at x = 0) =


=


=


=


= Not Defined [since 0<m<1]


(RHD at x = 0) =


=


=


=


= 0


Since , (LHD at x = 0)(RHD at x = 0)


Hence, f(x) is continuous at x = 0 but not differentiable.


More from this chapter

All 64 →
6

Find whether the following function is differentiable at x = 1and x= 2 or not:

f(x) =

7

Show that the function F(x) = is

Differentiable at x = 0, if m > 1.

 7

Show that the function F(x) = is

Neither continuous and nor differentiable, if m≤0.

 8

Find the values of a and b so that the function

f(x) =


is differentiable at each x € R.