Find the values of a and b so that the function
f(x) =

is differentiable at each x € R.

Question

Find the values of a and b so that the function f(x) = is differentiable at each x € R.

Philoid · Accepted Answer

For differentiability at x = 1,

LHD(at x = 1) = RHD(at x = 1)

(LHD at x = 1) =

=

= - 5

(RHD at x = 1) =

=

= b

Since, f(x) is differentiable , So

(LHD at x = 1) = (RHD at x = 1)

-5 = b

F(1) = 1 + 3 + a

= 4 + a

LHL =

=

RHL =

=

= b + 2

Find the values of a and b so that the functionf(x) = is differentiable at each x € R.