Without graphing, determine the average rate of change for the function f(x)=x^4 on the intervals below:

Question

1. -1 ≤ x ≤ 1
2. -2 ≤ x ≤ 2
3. -10 ≤ x ≤ 10

What can you notice about the answers found for the intervals above? Why did that happen? If possible, graph the function and suggest why this behaviour occurs.

Answer 1

(f(b) - f(a))/(b - a)

1. ((-1)⁴ - 1⁴)/(1 - (-1)) = (1 - 1)/2 = 0/2 = 0

The others are on you. Remember that a negative number raised to an even exponent results in a positive result.

Go!