Find the point x y on the graph of y squareroot x nearest t

Find the point (x, y) on the graph of y - squareroot x nearest the point (4, 0).

Given that:

Curve:

Y =x

and Line L joining this curve and the point (4, 0)

Let’s assume Line L touch curve at point P ( x, y)

Point the coordinate of P = (x, y) = (x,x) Given ( y= x)

Therefore Distance L = (x-4)²+(x-0)²)

L = (x²-7x+16) .... (Let equation A)

differentiate this with respect x

dL/dx = 1/2 ( (2x-7)/(x²-7x+16))

For Minimum L we put dL/dx = 0

1/2 ( (2x-1)/(x²-7x+16)) = 0

2x-7= 0

x= 7/2

therefore at x=7/2 this L would be minimum

therefore coordinates y = x = (7/2) = 1/2

Point P (x, y) = ( 7/2 , (7/2)) would be nearest point on the curve to the point (4,0)

annswer = (7/2 , (7/2) )