Let Q = (0,4) and R= (12,8) 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. (Before proceeding with this problem, draw a picture!) 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=. We find that f(x) has only one critical point in the interval at x= where f(x) has value Since this is smaller than the values of f(x) at the two endpoints, we conclude that this is the minimal sum of distances.

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Let Q = (0,4) and R= (12,8) 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. (Before proceeding with this problem, draw a picture!) 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=. We find that f(x) has only one critical point in the interval at x= where f(x) has value Since this is smaller than the values of f(x) at the two endpoints, we conclude that this is the minimal sum of distances.

Calculus1
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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have you tried this ? do you know distance formula to get PQ and PR ?
YOU'RE NOT EVEN GOKU HOW DARE YOU USE HIS PICTURE HE WAS MY ONLY FRIEND AS A CHILD
Who is Goku...

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since this is not related to question, please continue in private messages/chat...
I found where a similar problem was worked, but didn't quite understand what their numbers meant PQ = √[(x-0)2 + (0-6)2] = √(x2 + 36) PR = √[(x-6)2 + (0-7)2] = √(x2 - 12x + 85) f(x) = √(x2 + 36) + √(x2 - 12x + 85)
Distance between points (x1,y1) and (x2,y2) is \(\huge d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\) does this help ??
It does, so I have everything figured out except how you find what b=
never mind I got it Thanks for the help!
good :) ask if any further doubts...

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