Rate of Change (Algebraic) Math Example 2

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Example 2

medium

Find the average rate of change of

f(x) = x^2

from

x = 1

x = 4

Solution

1
Calculate $f(1) = 1$ and $f(4) = 16$ .
2
Average rate of change = $\frac{f(4) - f(1)}{4 - 1} = \frac{16 - 1}{3} = \frac{15}{3} = 5$ .
3
The function increases at an average rate of 5 units per unit of $x$ .

Answer

5

The average rate of change between two points equals the slope of the secant line connecting those points. For nonlinear functions, this rate varies depending on the interval.

About Rate of Change (Algebraic)

The ratio of how much one quantity changes to how much another quantity changes — measured over an interval.

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More Rate of Change (Algebraic) Examples

Example 1 easy

A car travels 150 miles in 3 hours. What is its average rate of change (speed)?

Example 3 easy

A plant grows from 5 cm to 17 cm in 4 weeks. What is the average growth rate?

Example 4 hard

Find the average rate of change of [formula] from [formula] to [formula].

← All Rate of Change (Algebraic) Examples Rate of Change (Algebraic) Concept

Related Concepts

Slope Derivative