Chapter 11, Problem 12CR

To determine

To graph: The function of $f\left(x\right)=x^3-3x-5$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=x^3-3x-5$

Graph:

Consider the function $f\left(x\right)=x^3-3x-5$

The graph for the given functions $f\left(x\right)=x^3-3x-5$ is shown in figure (1).

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Figure (1)

From the graph, we can see that the function has local minima and local maxima.

The function has one real zero and two imaginary zeros. The real zero has been marked in the above sketched graph. The imaginary zeros cannot be marked. The coordinates of the minima of the function are $\left(1,3\right)$ and the coordinates of the points of maxima are $\left(-1,7\right)$ .

The minimum value of the function is attained at $\left(1,3\right)$ and the maximum value of the function is attained at $\left(-1,7\right)$ .

The function can be seen as increasing in the range $(-\infty ,-1]$ decreasing on the interval $\left(-1,1\right)$ and increasing again the interval $[1,\infty )$ .

All the result obtained.

Interpretation: Graph for the functions $f\left(x\right)=x^3-3x-5$ shows in figure (1).