Question

Find the point P on the graph of the function y=sqrt{x} closest to the point (3,0)

Answer 1

'The x coordinate of P is:'

Answer 2

Find the distance of the point (x,y) on the curve to the point (3,0)
substitute y with sqrt(x)
Minimize the distance by finding the derivative with respect to x, equating it to 0 and solving for x.

Answer 3

Distance between (x,y) and (3,0) is:
D = sqrt{ (x-3)^2 + y^2 }
y = sqrt(x)
y^2 = x
put this in D
D = sqrt{ (x-3)^2 + x } = sqrt(x^2 - 6x + 9 + x}
D = sqrt(x^2 - 5x + 9)
Minimize D by finding the derivative with respect to x, equating it to 0 and solving for x.

Answer 4

answering someone else. will be right back.

Answer 5

Thank you

Answer 6

D = sqrt(x^2 - 5x + 9)
To minimize, find derivative and set it to 0.
D' = 1/2(x^2 - 5x + 9)^(-1/2) * (2x - 5) = 0
D' will be zero when numerator = 0
2x - 5 = 0
x = 5/2
Put x = 5/2 back in y=sqrt{x}
y = sqrt(5/2)

So the point on the curve that is closest to the point (3,0) is:
(5/2, sqrt(5/2))

Answer 7

In decimal, the point will be (2.5, 1.58)

Answer 8

Thank you so much, I'm going to "fan" you haha

Answer 9

you are welcome. glad to be able to help.