1. ## Delta Calculations

Note that if f(x) = x^2, then Δ f(x) = 2x +1. Beginning with this observation, modify it to find that a function g(x) such that Δ g(x) = x+1 and g(0) = 0. Show calculations.

2. ## Re: Delta Calculations

Originally Posted by azollner95
Note that if f(x) = x^2, then Δ f(x) = 2x +1. Beginning with this observation, modify it to find that a function g(x) such that Δ g(x) = x+1 and g(0) = 0. Show calculations.
As written this is a nonsense question.

3. ## Re: Delta Calculations

Originally Posted by azollner95
Note that if f(x) = x^2, then Δ f(x) = 2x +1. Beginning with this observation, modify it to find that a function g(x) such that Δ g(x) = x+1 and g(0) = 0. Show calculations.
Haven't we been through this before?

Calculating Delta Δ

What is the exact meaning of $\Delta f(x)$ in the context of this problem and your prior problem posted in the above link?

4. ## Re: Delta Calculations

I expect that Δ f(x) is the "unit difference operator", f(x+ 1)- f(x). The problem is to find a function, g, such that g(x+ 1)- g(x)= x+ 1. Using f as a guide, I would look for a function of the form $ax^2+ bx+ c$.

5. ## Re: Delta Calculations

skeeter you're ruthless haha. I cannot see the parallels in these two questions, all I know is that the confusion for in this question is at an all time high.

6. ## Re: Delta Calculations

Originally Posted by azollner95
skeeter you're ruthless haha. I cannot see the parallels in these two questions, all I know is that the confusion for in this question is at an all time high.
I am not amused. Why don't you just tell what the h__ $~~\Delta f(x)$ means?
I can get up now, walk over to my books and find five books having different definitions.
Hallofivy gave one hgood guess, but why do you expect us to guess?

7. ## Re: Delta Calculations

Looking through other examples that used this delta, it appears that it is calculating the derivative. However, wouldn't the derivative of x^2 be 2x and I know that the derivative of a constant 0? I am confused about where the +1 is coming from.

Would g(x) simply equal x? Since g(0) would equal 0 in that case.

8. ## Re: Delta Calculations

That is exactly why I suggested that it is the unit difference operator. Where did you get this problem? If it was from a text book then there should be a definition of $\Delta f$.

9. ## Re: Delta Calculations

This was part of a problem set that our professor assigned. We have no tutors nor a textbook. Looking through my notes the only thing I have on it is that delta g(x) = g(x+1) -g(x)....... but I am not sure how to apply that knowledge.

10. ## Re: Delta Calculations

Originally Posted by azollner95
Note that if f(x) = x^2, then Δ f(x) = 2x +1. Beginning with this observation, modify it to find that a function g(x) such that Δ g(x) = x+1 and g(0) = 0. Show calculations.
Originally Posted by azollner95
This was part of a problem set that our professor assigned. We have no tutors nor a textbook. Looking through my notes the only thing I have on it is that delta g(x) = g(x+1) -g(x)....... but I am not sure how to apply that knowledge.
Reading the original post at face value then
\begin{align*}\Delta f(x)&=f(x+1)-f(x)\\&=(x+1)^2-x^2 \\&=x^2+2x+1-x^2\\&=2x+1 \end{align*}

Is that what you expect it is?