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

Question

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

• -1≤ x ≤ 1

• -2 ≤ x ≤ 2

• -10 ≤ x ≤ 10

What do you notice about your answers from the above intervals? Why do you think that happened?

Graph the function and postulate why this behaviour occurs.

Answer 1

It is an even function which means f(x)=f(-x)

For every element ,x, in the domain.

The Average Rate of change.A.R.O.C is

[ f(b)-f(a) ]/ (b-a) for continuous function on interval [a,b]

For a=-b, the numerator in the formula will be zero,

Since f(b)-f(a)=f(b)-f(-b) <--- substitution

= f(b)-f(b)=0 <--- even function

While the denominator shall be [2b]

Therefore A.R.O.C is ZER0