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

Distance between (x,y) and (3,0) is:

D = sqrt{ (x-3)^2 + y^2 }

y = sqrt(x)

y^2 = x

Then substitute D,  that would be

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.

D = sqrt(x^2 - 5x + 9)

find derivative and set it to 0 in order to minimize D

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)

the points of the curve that is nearest to  (3,0) will be (5/2, sqrt(5/2))

So the answer will be  (2.5, 1.58)

step-by-step explanation: