Answer:
Refer the attached figure.
Step-by-step explanation:
Given : Equations \(y=x^3\) and \(y=\frac{16}{x}\)
To find : Graph both the equations and Use the graphs to find the exact solutions to the equation \(x^3=\frac{16}{x}\)
Solution :
Let, \(y=x^3\) ........[1]
\(y=\frac{16}{x}\) .......[2]
Now, we plot these two equations.
The graph of \(y=x^3\) is shown with green line.
The graph of \(y=\frac{16}{x}\) is shown with violet line.
Now, using the graph,
The solution to this system will be their intersection point.
The intersection points are (2,8) and (-2,-8).
If we substitute y from [1] equation into [2]
We get, \(x^3=\frac{16}{x}\)
Refer the attached figure below.
