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heradog
 2 years ago
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 xaxis 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.
heradog
 2 years ago
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 xaxis 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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hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1have you tried this ? do you know distance formula to get PQ and PR ?

yololol
 2 years ago
Best ResponseYou've already chosen the best response.0YOU'RE NOT EVEN GOKU HOW DARE YOU USE HIS PICTURE HE WAS MY ONLY FRIEND AS A CHILD

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1since this is not related to question, please continue in private messages/chat...

heradog
 2 years ago
Best ResponseYou've already chosen the best response.0I found where a similar problem was worked, but didn't quite understand what their numbers meant PQ = √[(x0)2 + (06)2] = √(x2 + 36) PR = √[(x6)2 + (07)2] = √(x2  12x + 85) f(x) = √(x2 + 36) + √(x2  12x + 85)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1Distance between points (x1,y1) and (x2,y2) is \(\huge d=\sqrt{(x_1x_2)^2+(y_1y_2)^2}\) does this help ??

heradog
 2 years ago
Best ResponseYou've already chosen the best response.0It does, so I have everything figured out except how you find what b=

heradog
 2 years ago
Best ResponseYou've already chosen the best response.0never mind I got it Thanks for the help!

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1good :) ask if any further doubts...
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