Question

Find the minimum distance from the point (3,0) to y= square root of x

Answer 1

this one easier. any point on the graph will look like

\[(x,\sqrt{x})\] and working with the square of the distance we see that you want to minimize
\[(x-3)^2+(\sqrt{x}-0)^2\] or simply
\[(x-3)^2+x\]

Answer 2

don't really even need calc for this. you have
\[f(x)=(x-3)^2+x=x^2-5x+9\] minimum value at the vertex, or else take the derivative, set it equal zero, etc

Answer 3

okay thanks again

Answer 4

yw