How do you find the average rate of change of f(x)=2x2 over the interval [1, 5]?

The average rate of change is simply the incremental ratio calculated over the whole interval, that is:C―=f(b)−f(a)b−aIn this case:C―=[252]+[212]5−1=14(225+2)=1325Result:The average rate of change is C―=1325

f(x)=2x2,[1,5][a,b] is f(b)−f(a)b−aWe have: a=1, b=5, f(x)=2x2Thus, f(b)−f(a)b−a=2(5)−2−(21−2)5−(1)=−1225.Answer: =−1225

The average rate of change is simply the incremental ratio calculated over the whole interval, that is:C―=f(b)−f(a)b−aIn this case:C―=[252]+[212]5−1=14(225+2)=1325Result:The average rate of change is C―=1325

f(x)=2x2,[1,5][a,b] is f(b)−f(a)b−aWe have: a=1, b=5, f(x)=2x2Thus, f(b)−f(a)b−a=2(5)−2−(21−2)5−(1)=−1225.Answer: =−1225

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

High School
Calculus and Analysis
Calculus 1
Derivatives

Jasiah Vincent

Answered question

2022-04-14

How do you find the average rate of change of

f (x) = \frac{2}{x^{2}}

over the interval [1, 5]?

Answer & Explanation

pobijedi6wro

Beginner2022-04-15Added 15 answers

The average rate of change is simply the incremental ratio calculated over the whole interval, that is:

\overset{―}{C} = \frac{f (b) - f (a)}{b - a}

In this case:

\overset{―}{C} = \frac{[\frac{2}{5^{2}}] + [\frac{2}{1^{2}}]}{5 - 1} = \frac{1}{4} (\frac{2}{25} + 2) = \frac{13}{25}

Result:
The average rate of change is

\overset{―}{C} = \frac{13}{25}

uvredio0of6

Beginner2022-04-16Added 17 answers

f (x) = \frac{2}{x^{2}}, [1, 5]

[a,b] is

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

We have: a=1, b=5,

f (x) = \frac{2}{x^{2}}

Thus,

\frac{f (b) - f (a)}{b - a} = \frac{2 {(5)}^{- 2} - (21^{- 2})}{5 - (1)} = - \frac{12}{25}

.
Answer:

= - \frac{12}{25}

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