Question

find point P on the graph of the equation y=sqrt(x) closest to the point (5,0)

Answer 1

i got 2/9 i dont know where i made a mistake

Answer 2

a point on the curve looks like \((x,\sqrt{x})\)
the square of the distance to (5,0) will be \[(x-5)^2+\sqrt{x}^2=x^2-10x+25+x\]
\[=x^2-9x+35\]
find the minimum values of this quadratic

Answer 3

sorry that lasts line should have been \[x^2-9x+25\]

Answer 4

i see where my mistake is

Answer 5

good from there?

Answer 6

just solve the quadratic and plug in the values to see which one is the minimum right?

Answer 7

minimum is at the vertex, find it via \(-\frac{b}{2a}\)

Answer 8

that is why the answer is \(\frac{9}{2}\)