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Chapter 1: Problem 66

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y=(6-x) \sqrt{x}$$

Short Answer

Expert verified
Based on the graph, it appears that there are intercepts around x = 0 and x = 6. The exact values may vary slightly depending on the accuracy of the graphing utility. To get more precise results, you can use numerical methods or solve the equation analytically.

Step by step solution

01

Problem Analysis

Let's start by analyzing the equation: \(y = (6-x)\sqrt{x}\). It can be seen as a product of two sub-functions, \(6-x\) and \(\sqrt{x}\). The function \(6-x\) is a linear function which decreases with increasing x, and \(\sqrt{x}\) is a square root function which rises more slowly as x increases. Therefore, their product will likely exhibit behavior of both types of functions. The intercepts occur at the x-values for which y is zero.
02

Graphing the Function

The next step is to graph the equation using a graphing utility. This can be done by entering the equation in the y= menu of the graphing calculator and using standard window settings. By inspecting the graph, it becomes clear where the curve meets or crosses the x and y axes.
03

Finding Intercepts

Finally, approximate the intercepts. These are the points on the x-axis and y-axis where the function crosses or touches. To get a rough approximation, identify the points on the graph where the curve appears to intersect the axes.

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