Chapter 12.4, Problem 7E

(a)

To determine

To graph: The function $f\left(x\right)=2x^3+3x^2-12x+1$ and find the x intercept by technology. Also, indicate the $x$ and $y$ intercepts in the graph.

(b)

To determine

To calculate: The points of extrema for the provided function $f\left(x\right)=2x^3+3x^2-12x+1$. Also, indicate it on the graph of the function.

(c)

To determine

To calculate: The points of inflection for the provided function $f\left(x\right)=2x^3+3x^2-12x+1$. And, indicate the points in the graph of the function.

(d)

To determine

To graph: The function $f\left(x\right)=2x^3+3x^2-12x+1$ indicating the behavior near the singular point of the function.

(e)

To determine

To graph: The function $f\left(x\right)=2x^3+3x^2-12x+1$ indicating the behavior at infinity. Also, verify the graph by the use of technology.