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Chapter 10: Problem 11

Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement. HINT [See Example 1.] $$ \text { Interval: }[0,4] $$

Short Answer

Expert verified
The average rate of change of the function \(f(x)\) over the interval [0, 4] is \(\frac{f(4) - f(0)}{4}\) (units if given).

Step by step solution

01

Identify the function and interval

The first step is to recognize the function to work with, which is not provided in the exercise. We will use a general $$f(x)$$ function here. The interval given is [0, 4], which means we will find the average rate of change between the points when $$x = 0$$ and $$x = 4$$.
02

Calculate f(0) and f(4)

Initially, we need to evaluate the function at the endpoints of the interval. Calculate the function values at $$x = 0$$ and $$x = 4$$: $$ f(0) = f(0)\\ f(4) = f(4) $$
03

Compute the average rate of change

Now, we'll calculate the average rate of change of the function by using the following formula: $$ \text{Average rate of change} = \frac{f(4) - f(0)}{4 - 0} $$ Substitute the calculated values of $$f(0)$$ and $$f(4)$$ into this formula: $$ \text{Average rate of change} = \frac{f(4) - f(0)}{4} $$
04

Specify units of measurement if appropriate

If the given function has any specific units of measurement, mention them along with the calculated average rate of change. In this case, as no specific function was given, we cannot mention any units of measurement. The final answer should be in the form: $$ \text{Average rate of change} = \frac{f(4) - f(0)}{4} \text{ (units if given)} $$

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Most popular questions from this chapter

Compute the derivative function \(f^{\prime}(x)\) algebraically. (Notice that the functions are the same as those in Exercises \(1-14 .)\) HINT [See Examples 2 and \(3 .]\) $$ f(x)=-2 x+4 $$

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