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Home > CALC > Chapter 1 > Lesson 1.3.3 > Problem 1-128


While studying the finite differences of a particular function, Neo noticed that the differences changed linearly. What can you tell him about the original function? Also, how do his finite differences change?

A linear changing difference is a difference that increases or decreases in greater amounts each time. For example, if , , , , then the differences are , and , respectively, and changing linearly, in this case with the linear rule, . What kind of function has this kind of change?

The original function is quadratic.

Take a quadratic function and list out some successive differences. For example, let's take the differences from the earlier hint: , , and . What is the difference between these differences and how do they change? If they don't change, what is the term for that?

The differences of the differences are constant.