Find the point on the curve y = √ 2 x + 4 which is closest to the point ( 3 , 0 ) .

Here you'll need differential calculus.

The distance between (3,0) and (x, sqrt(2)*x + 4) is given by the distance formula:

distance:  sqrt [ (3+x)^2 + (sqrt(2)*x + 4)^2 ]

Differentiate this, and then set the resulting derivative = to 0.  Solve for x.  Test your results to ensure that the distance d is actually the SMALLEST, given the root(s) x that you've found.

Write the coordinates of this point on the curve as ( x, f(x) ).