Chapter 2.3, Problem 37E

a.

To determine

To find the local maximum and local minimum of the function

Explanation of Solution

Given information : the function is $g\left(x\right)=x^4-2x^3-11x^2$ .

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression $x^4-2x^3-11x^2$ which is required to graph.

Step 4: Press $\boxed{\text{GRAPH}}$ button to graph the function.

Step 5: Using $\boxed{\text{TRACE}}$ feature on the calculator

The graph is obtained as:

  

From the above graph, it can be observed that the local maximum $\approx 0$ when $x\approx 0$ and the local minimum $\approx -13.6$ when, local minimum $\approx -73.3$ when $x\approx 3.2$

b.

To determine

To find the interval on which the function is increasing and on which the function is decreasing up to two decimal

Answer to Problem 37E

The function $f$ is decreasing on $(-\infty ,-1.7]\cup [0,3.2]$ and increasing on $\left[-1.7,0\right]\cup [3.2,\infty )$ .

Explanation of Solution

Given information :

The function is $g\left(x\right)=x^4-2x^3-11x^2$ .

The graph of the function is obtained as:

  

Using $\boxed{\text{TRACE}}$ feature on the calculator,

From the above graph, it can be observed that the function $f$ is decreasing on $(-\infty ,-1.7]\cup [0,3.2]$ and increasing on $\left[-1.7,0\right]\cup [3.2,\infty )$