Chapter 3.6, Problem 7CFU

To determine

To find:and classify the extrema of the function by using graphing calculator to graph the function.

Answer to Problem 7CFU

Relative minimum point = $\left(0,-2\right)$

Absolute minimum point = $\left(-2.25,-10.543\right)$

Explanation of Solution

Given information:

  $g\left(x\right)=x^4+3x^3-2$

Calculation:

The graph for the given function is as follows:

  

There is no maximum point. At $x=0\text{ and }-2.25$ , the graph is decreasing on the left and increasing on the right. The values of minimum are $\left(0,-2\right)\text{ and }\left(-2.25,-10.543\right)$ . Since, $\left(-2.25,-10.543\right)$ has the lowest point of the function. Thus, $\left(-2.25,-10.543\right)$ is the absolute minimum, and $\left(0,-2\right)$ is relative minimum point.