How do you find the average rate of change of f(x)=3x−2 over the interval [4,7]?

The average rate of change of a function f over an interval [a,b] isf(b)−f(a)b−a.For this question, we have f(x)=3x−2 and [a,b]=[4,7]So the average rate of change isf(7)−f(4)7−4=37−2−34−23=35−323=3⋅25⋅2−3⋅52⋅53=6−151031=−91031=−910⋅13=−310

Solved: "How do you find the average rate of..."

High School
Calculus and Analysis
Calculus 1
Derivatives

Abbey Ellison

Answered question

2022-04-13

How do you find the average rate of change of

f (x) = \frac{3}{x - 2}

over the interval [4,7]?

Answer & Explanation

carlosegundoacyg

Beginner2022-04-14Added 10 answers

The average rate of change of a function f over an interval [a,b] is

\frac{f (b) - f (a)}{b - a}

.
For this question, we have

f (x) = \frac{3}{x - 2}

and [a,b]=[4,7]
So the average rate of change is

\frac{f (7) - f (4)}{7 - 4} = \frac{\frac{3}{7 - 2} - \frac{3}{4 - 2}}{3}

= \frac{\frac{3}{5} - \frac{3}{2}}{3} = \frac{\frac{3 \cdot 2}{5 \cdot 2} - \frac{3 \cdot 5}{2 \cdot 5}}{3}

= \frac{\frac{6 - 15}{10}}{\frac{3}{1}} = \frac{\frac{- 9}{10}}{\frac{3}{1}}

= \frac{- 9}{10} \cdot \frac{1}{3} = - \frac{3}{10}

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