Find the point on the curve y Squarerootx that is closest t

Find the point on the curve y = Squarerootx that is closest to the point (3, 0).

Solution

Let the point be ( x, y)

D = sqrt[(x -3)^2 + y^2]

= sqrt[(x -3)^2 +x ]

find derivative of D :

dD/dx = [ 2(x -3) +1]/2sqrt[(x -3)^2 +x ]

d/D/dx = 0 ; 2(x -3) +1 =0

2x - 5 =0

x = 5/2 = 2.5

y = sqrt(5/2) = + 1.58

we have ( 2.5 , 1.58)

The point on the curve is ( 2.5 , 1.58)