Chapter 5.4, Problem 4E

(a)

To determine

To graph: The function $g\left(x\right)=2x^3-6x$ in the domain $\left[-4,4\right]$ and locate the x and $y$ intercepts of the function.

(b)

To determine

To calculate: The points of extrema for the provided function $g\left(x\right)=2x^3-6x$.

(c)

To determine

To calculate: The points of inflection for the provided function $g\left(x\right)=2x^3-6x$. And, locate it on the graph.

(d)

To determine

To graph: The function $g\left(x\right)=2x^3-6x$ indicating the behavior near the singular point of the function.

(e)

To determine

To graph: The function $g\left(x\right)=2x^3-6x$ indicating the behavior at infinity. Also, verify the graph by the use of technology.