Short Answer

Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [−4, 4], and illustrate this average value as a height on the graph.

The solution is $9 .$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

We are given with a function f and its graph.

The objective is to estimate the area of f on [-4,4].

Step 2. Calculation

Consider the rough approximation for the function given in the diagram.

The values of the functions are at $f (0) = 54 a n d f (3) = 0$

Then, the rough value for the average can be calculated as shown below.

$= \frac{1}{4 - (- 4)} \int_{- 4}^{4} (54 - 18 x) d x = \frac{1}{8} {[54 x - 9 x^{2}]}_{- 4}^{4} = \frac{1}{8} [216 - 144 + 216 + 144] = \frac{1}{8} (432) = 9$

Thus, the rough value for the average is $9 .$

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Calculus

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Short Answer

Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [−4, 4], and illustrate this average value as a height on the graph.

Step by Step Solution

Step 1. Given information

Step 2. Calculation

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Calculus

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Short Answer

Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [−4, 4], and illustrate this average value as a height on the graph.

Step by Step Solution

Step 1. Given information

Step 2. Calculation

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