Question

Find the coordinates of the point on the curve y= tanx that is closest to the point (1,1)
please help me

Answer 1

Minimize the distance formula and solve for x and then use tan(x) to find y.

Answer 2

Have you sketched the graph of y=tan x, at least between x=-pi/2 and x=pi/2, as well as the poin (1,1)? Once you have a sketch, estimate by eye where that point on the curve y=tan x will be to result in the shortest distance.

Then, set up the distance formula appropriately, as MaleVolence has suggested. Questions? Please ask.

Answer 3

do i need to plug anything into the distance formula before taking the derivative of the distance formula?

Answer 4

yes i have sketched the graph

Answer 5

Note that every point on that graph has the coordinates (x, tan x). Make sense to you?

Answer 6

yes.

Answer 7

Greaet. So you want to set up a formula for the distance between the point (x, tan x) on the graph and the fixed point (1,1).

Once you have this distance formula, you can minimize the distance in the usual way.
Questions? Comments?

Answer 8

should i put 1 as x subscript 2 or x subscript 1?

Answer 9

That order makes no difference.

Answer 10

write an equation that looks something like D(x)=Sqrt( (x-1)^2 + (tan x -1)^2 ).
You could either differentiate this immediately, or you could square both sides to elim. the Sqrt operator. Once you have the deriv ., set the whole deriv = to 0 and solve for x.

Answer 11

Please message me if you need further help with this problem. I'd like to get off the computer now or very soon. Any last minute questions?

Answer 12

Please don't feel let down, but I'm signing off now, with the understanding that I'll be glad to message y ou or engage in this live dialogue later.

Answer 13

Your question: "do i need to plug anything into the distance formula before taking the derivative of the distance formula?" Answer: yes. see above:

"write an equation that looks something like D(x)=Sqrt( (x-1)^2 + (tan x -1)^2 )"

Answer 14

no more questions, thank you :)