07-09-2019, 01:38 PM
(This post was last modified: 07-09-2019, 01:57 PM by MrBossmanJr.)

Well, this gets into proofs and definitions, but first let's cite the extreme value theorem. The extreme value theorem states that if a function is continuous on an interval that is closed, then the function must have or contain a minimum and a maximum on the interval. This can be written as f© <= f(x) <= f(d), where c is the lowest point and d is the highest point on the x-axis and f© and f(d) on the y-axis respectively.

You are stating that it has no minimum or maximum so it has to be a straight line from left to right based on the interval. Therefore all the values are equal and it means that the requirements of that statement, f© <= f(x) <= f(d), is met.

EDIT: So take straight line values that is 1. 1 is less than or equal to 1 which is less than or equal to 1. I think this is what you mean or wanted.

And, why do the Pythagorean theorem?

You do the theorem because you have the x and y values of velocity or in this case speed. You want to find the two dimensional value of that object. This ties into mechanical physics. If an object is moving x with a certain amount of speed (2 ft/s) and y with a certain amount of speed (4 ft/s), then you know it isn't just going in one direction. Not just x or just y; it is moving in both directions at the same time. It's hard to come up with an example since I'm not a professor lol. For every second, it is moving 2 feet along the x-axis (right) and 4 feet along the y-axis (up). Can you see how it isn't moving just one direction at a time? You need to find where it is actually going and the pythagorean theorem helps you calculate that diagonal speed.

You are stating that it has no minimum or maximum so it has to be a straight line from left to right based on the interval. Therefore all the values are equal and it means that the requirements of that statement, f© <= f(x) <= f(d), is met.

EDIT: So take straight line values that is 1. 1 is less than or equal to 1 which is less than or equal to 1. I think this is what you mean or wanted.

And, why do the Pythagorean theorem?

You do the theorem because you have the x and y values of velocity or in this case speed. You want to find the two dimensional value of that object. This ties into mechanical physics. If an object is moving x with a certain amount of speed (2 ft/s) and y with a certain amount of speed (4 ft/s), then you know it isn't just going in one direction. Not just x or just y; it is moving in both directions at the same time. It's hard to come up with an example since I'm not a professor lol. For every second, it is moving 2 feet along the x-axis (right) and 4 feet along the y-axis (up). Can you see how it isn't moving just one direction at a time? You need to find where it is actually going and the pythagorean theorem helps you calculate that diagonal speed.

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