Q7 of 64 Page 10

Show that the function F(x) = is

Differentiable at x = 0, if m > 1.

f(x) =


(LHD at x = 0) =


=


=


=


=


=


= 0 * k [when - 1]


(RHD at x = 0) =


=


=


= = 0


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


Hence, f(x) is differentiable at x = 0


More from this chapter

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5

Discuss the continuity and differentiability of f(x) = |x| + |x - 1| in the interval ( - 1,2).

 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

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

 7

Show that the function F(x) = is

Neither continuous and nor differentiable, if m≤0.