Question

Calculus q. Find the point on the graph of the function that is closest to the given point. f(x)=(square root of (2)) (4,0)

Answer 1

\[\large f(x)=\sqrt{2x}\] maybe?

Answer 2

where did the 2x come from?

Answer 3

I thought wolfram might help, but not quite. it just tells me the equation. I guess I'm not much of a help heh.

Answer 4

In the general case, you want to find the distance between the point \((x, f(x))\) and \((x_0, y_0)\), you'd first use the distance formula:\[
d(x) =\sqrt{(x_0-x)^2+(y_0-f(x))^2}
\]Then you want to minimize, \(d(x)\). That is, find the point where \(d'(x)=0\) and \(d''(x)>0\)

Answer 5

But in order to do this, you need \(f(x)\)

Answer 6

okay

Answer 7

What is \(f(x)\)?

Answer 8

isn't that the function?

Answer 9

Yeah, @lilly21 is \(f(x)=\sqrt{2}\) ?

Answer 10

yes :]

Answer 11

Since \(0-\sqrt{2}\) isn't going to change, you wanna minimize \(4-x\)

Answer 12

Since \(4-x=0\) when \(x = 4\). We want 4.

Answer 13

can u pleaz explain> plz?