How do I find the Average Rate of Change?

Question

If f(x) = 2x⁴ -x +1, what is the average rate of change between x₁ = -3 and x₂ = 0?

How can I find the solution to this equation and others similar to it?

Answer 1

Average rate of change is an important but simple concept in calculus, and it is an old friend from, like, 7th grade math:

Avg rate of change of f(x) on [-3 , 0] = (f(0) - f(-3)) / (0 - (-3)).

In other words, (y₂ - y₁) / (x₂ - x₁).