Optimization problem
Find the point on the graph of f(x)=square root of (-x+8) so that the point (2,0) is closest to the graph.

Question

Optimization problem
Find the point on the graph of f(x)=square root of (-x+8) so that the point (2,0) is closest to the graph.

precal · Answer

$$f(x)=\sqrt{-x+8}$$

precal · Answer

I found the derivative of f (x) but not sure what else to do with this information

precal · Answer

$$f ' (x)=\frac{ 1 }{ 2\sqrt{-x+8} }$$

precal · Answer

@ganeshie8

precal · Answer

@SolomonZelman

solomonzelman · Answer

I am not so good at these. https://www.desmos.com/calculator/ixbpyipjp7

precal · Answer

thanks

solomonzelman · Answer

What, helped ?

precal · Answer

not really

solomonzelman · Answer

Ohh, I tried... sorry-:(

precal · Answer

no problem, I have to show work using calculus

precal · Answer

@jim_thompson5910

precal · Answer

@dumbcow

precal · Answer

sorry I gotta go pick up my tadpoles, I really appreciate any help. I will read the comments later

dumbcow · Answer

ok you want to minimize distance from (2,0) to (x,f(x))

so first use distance formula

$$d = \sqrt{(x-2)^2 + (8-x)} = \sqrt{x^2 -5x+12}$$
its this function d(x) that you want to take derivative of
$$d'(x) = \frac{2x-5}{2 \sqrt{x^2 -5x+12}} = 0$$
$$x = \frac{5}{2}$$

anonymous · Answer

might i make a small suggestion?

anonymous · Answer

it is always easier to work with the square of the distance rather than the distance

precal · Answer

@dumbcow @satellite73 how does f(x) play into this?