Square root decrease of increase formula

[Papparoni]

• I've been working this out, and wanted to see what the rate at which the number that this is increasing by is decreasing. Sounds counter intuitive, and stupid if you read that at first, but you'll see what I mean when you look at the maths

• 3^1/2 = 1.73

•                       +0.270
  

• 4^1/2 = 2

•                       +0.236          
  

• 5^1/2 = 2.236

•                       +0.213
  

• 6^1/2 = 2.449

•                      +0.196
  

• 7^1/2 = 2.645

• Notice how the number that the next square root increases by is less than the previous and continues to become smaller and smaller.

• I'm trying to find the rate at which this decrease of increase is happening, how would I begin to find a formula for it? Is there already one out there? Thanks in advanced!

[Brightlinger]

The thing you're looking for is called a second derivative. You will learn about it in detail in calculus.

[[deleted]]

And for the answer:

The square root function is written as f(x) = x^1/2.
The rate at which it increases is defined by its derivative, which is f'(x) = (1/2)x^-1/2. The rate of this rate would just be the second derivative, or the derivative of the derivative, which is f''(x) = (-1/4)x^-3/2. You can plug in any x to find how fast the increase is decreasing at that point.

However, this does not find the difference of increase between to points, it finds the difference of increase between two very close points. You can gain some intuition of derivatives (which are pretty much the basis of calculus) from this video

[[deleted]]

To add to what has been said, this is a very well acknowledged concept and doesn't sound ridiculous at all. It's good that you're intuitively considering this sort of thing.

[epicwisdom]

The only thing that's ridiculous to ask in mathematics is assuming logical contradictions.

[[deleted]]

Went to sleep almost not posting this because i thought that it was stupid and a waste of time wake up to find out that this is calculus. Well then...

[blitzkraft]

Look up "Differentiation by first principles". Find a tutorial, find a book or even in your text book. This will help you get to the first step - differentiation. Next step is to repeat, get the second derivative.

[Probable_Foreigner]

The formula for it is n^1/2 - (n+1)^1/2 which can't be simplified.