Thread: Finding the distance between two points

Let Q = (0,5) and R = (10,6) be given points in the plane. We want to find the point P = (x,0) on the x axis such that the sum of distances PQ+PR is as small as possible.
To solve this problem, we need to minimize the following function of x: f(x) = ?
over the closed interval [A,B] where A = ? and B = ?

Originally Posted by derekjonathon

Let Q = (0,5) and R = (10,6) be given points in the plane. We want to find the point P = (x,0) on the x axis such that the sum of distances PQ+PR is as small as possible.
To solve this problem, we need to minimize the following function of x: f(x) = ?
over the closed interval [A,B] where A = ? and B = ?

find and minimize

Thank you for your help, I really appreciate it...

But I am still not getting what the technique is here to answer the question.

I understand finding distance (d1) and distance (d2)

but the derivative part has me thrown off. Also, I don't get what function is supposed to be minimized...

How do I go step by step through this?

Originally Posted by derekjonathon

Thank you for your help, I really appreciate it...

But I am still not getting what the technique is here to answer the question.

I understand finding distance (d1) and distance (d2)

but the derivative part has me thrown off. Also, I don't get what function is supposed to be minimized...

How do I go step by step through this?

minimize the function

start by finding , set the result equal to 0, and solve for the value of x that minimizes S.