, D ( )
0
′k
< Also when
2
1
c2
k
−
>
, then D ( )
0
′k
> So, by first derivative test, D (k) is minimum at 
2
1
c2
k
−
= Rationalised 2023-24
APPLICATION OF DERIVATIVES
169
Hence, the required shortest distance is given by
2
2
1
2
1
2
1
4
1
D
2
2
2
2
c
c
c
c
c
−
−
−
−




=
+
−
=








ANote  The reader may note that in Example 35, we have used first derivative
test instead of the second derivative test as the former is easy and short