How to find minimum distance between two graphs?

Question

If you have two graphs plotted on the same plane, how would you find the minimum distance between the two? Is there a rule or formula? Or is it depending on the individual graphs?

For example: minimum distance between y = (x+1)^2 and y = -1(x-1)^2 ?

I am trying to find the minimum distance between any one point on one graph and any one point on another graph. BOth of these graphs are plotted on the same plane.

Answer 1

This is actually a multivariable calculus question.

You do make use of the distance formula

In your example, you need to pick two points. One on the first graph and the other on the second graph. Call these points
(x1, y1) and (x2, y2)

d^2 = (y2 - y1)^2 + (x2-x1)^2

Substitute in for y2 and y1 the corresponding functions of x to get d in terms of two variables.

The function d is a function of two variables, which requires that you use multivariable calculus to minimize d. I am kind of rusty on multivariable calculus, though.

Answer 2

Are you talking about two seperate graphs or two seperate points on a graph?

To find the distance between points you need to use the distance formula...

Assuming you know each point...Let's say the first point is (-3, 7) and the second point is (5, -2). The first set is designated as x1
(-3) and y1 (7). The second set as x2 and y2. Knowing that, you just plug into the distance formula:

Distance equals the square root of (x2 - x1)^2 + (y2 - y1)^2...

So, in the above example, d=SR of (5-(-3))^2 + (-2-7)^2...

Do the math... D= SR of 145.

Hope this helps...

Answer 3

a straight line