Chapter 1.8, Problem 19PPS

To determine

To Sketch: The graph which is nonlinear $x$ Intercept at $-8$ and $-2$ and $y$ Intercept at $3$,relative minimum at $x=-6,x=6$ and relative maximum at $x=2$ , positive for $x<-8$ and $x>-2$ and the negative between $x=-8$ and $x=-2$ .

Answer to Problem 19PPS

  

Explanation of Solution

Given: To sketch the graph with the following characteristics

The Nonlinear graph has $x$ Intercept at $-8$ and $-2$ and $y$ Intercept at $3$ .The graph has relative minimum at $x=-6,x=6$ and relative maximum at $x=2$ . The graph is positive for $x<-8$ and $x>-2$ and the negative between $x=-8$ and $x=-2$ . As $x$ decreases, $y$ increases and as $x$ increases, $y$ increases

Since the graph has $x$ Interceptat $-8$ and $-2$ , it must cross the $x$ axis at $-8$ and $-2$ and $y$ Intercept is $3$ it must cross the $y$ axis at $3$ .

The graph is increasing for all values of $x$ , so it must going up left to right

The graph is positive for $x<-8$ and $x>-2$ therefore it must be above the $x$ axis.

The graph is negativebetween $x=-8$ and $x=-2$ therefore it must be below the $x$ axis.

The graph has relative minimum at $x=-6,x=6$ and relative maximum at $x=2$

The possible graph for the given characteristics is shown below