Solution:
We have
For to be continuous and differentiable in
must attain a constant value for all .
Clearly, this is possible only when
In that case, we have
which is continuous and differentiable.
Hence, the least value of is .
If the function ,[.] denotes the greatest integer function, is continuous and differentiable in (4, 6), then the least value of is
We have
For to be continuous and differentiable in
must attain a constant value for all .
Clearly, this is possible only when
In that case, we have
which is continuous and differentiable.
Hence, the least value of is .