Q3 of 64 Page 10

Show that is differentiable at x = 3. Also, find f’(3).

For differentiability,


LHD(at x = 3) = RHD (at x = 3)


(LHD at x = 3) =


=


=


=


=


= 12


(RHD at x = 3) =


=


=


=


=


=


= 12


Since, (LHD at x = 3) = (RHD at x = 3)


Hence, f(x) is differentiable at x = 3.


More from this chapter

All 64 →
1

Show that f(x) = |x - 3| is continuous but not differentiable at x = 3.

 2

Show that f(x) = is not differentiable at x = 0.

 4

Show that the function f defined as follows,

f (x) = rr 3x-2 , & 0<x less than equal to 3 2x^2 - x , & 1<x less than equal to 2 5x-4 , &x>2


Is continuous at x = 2, but not differentiable there at x = 2.

 5

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