Question

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.

Short answer

The solution is$9.$

Step-by-step solution

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 $f\left(0\right)=54andf\left(3\right)=0$

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

$$\begin{gathered} =\frac{1}{4-(-4)}{\int }_{-4}^4(54-18x)dx \\ =\frac{1}{8}{[54x-9x^2]}_{-4}^4=\frac{1}{8}[216-144+216+144] \\ =\frac{1}{8}\left(432\right) \\ =9 \end{gathered}$$

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