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 Example 24 Let AP and BQ be two vertical poles at
points A and B, respectively If AP = 16 m, BQ = 22 m
and AB = 20 m, then find the distance of a point R on
AB from the point A such that RP2 + RQ2 is minimum