# Suppose f(x) = 2x^{3}. Write an expression in terms of x and h that represents the average rate of change of f over any interval of length h. [That is, over any interval (x, x + h)] Simplify your answer as much as possible.

Jaya Legge 2021-02-01 Answered
Suppose $f\left(x\right)=2{x}^{3}.$ Write an expression in terms of x and h that represents the average rate of change of f over any interval of length h. [That is, over any interval (x, x + h)] Simplify your answer as much as possible.
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Obiajulu
Step 1
Consider the function:
$f\left(x\right)=2{x}^{3}$
The average rate of change of function over any intervals of length “h” is given by the formula,
Average rate
Step 2
The average rate of changes of the given function is,
Average rate

Hence the average rate of changes of the given function is