Question Number 102804 by bramlex last updated on 11/Jul/20

The coordinates of two points A  & B are (0,8) and (9,4)  respectively. The point P with  coordinate (p,0) lies on the  x−axis where 0<p<9. Let s  denotes the sum of the length of  two segments PA and PB . by  expressing s in terms of p  otherwise, show that (ds/dp) =  (p/(√(64+p^2 ))) − ((9−p)/(√(16+(9−p)^2 )))

Answered by bemath last updated on 11/Jul/20

s = PA +PB = (√(p^2 +64))  +(√((9−p)^2 +16))  (ds/dp) = ((2p)/(2(√(64+p^2 )))) +  ((2(9−p)(−1))/(2(√(16+(9−p)^2 )))) =  (p/(√(64+p^2 )))−(((9−p))/(√(16+(9−p)^2 ))) □