Chapter 6.4, Problem 34PPS

To determine

To solve:the given inequality by using a graph or algebraically.

Answer to Problem 34PPS

  $\left\{x|x<-6\text{ or }x>-2\right\}$

Explanation of Solution

Given:

The given inequalityis $x^2+8x+12>0$ .

Calculation:

The turning point in a given curve in the graph is defined as the relative minima or the relative maxima.

Consider the graph given in the question:

a.

  

Consider below given graph:

  

The x-coordinate of every turning point A, B, C and D isandrespectively.

The relative maximum is the point where the entire neighborhood is smaller than that point and similarly for the relative minima.

Hence, the relative maximum is atand the relative minimum is at.

b.

Consider below given graph:

  

The zeroes is the intersecting point of the curve over the-axis of the graph. Those points are A, B and C.

  

Hence, the required coordinates of the zeroes are.

c.

  

As, there are three real zeroes for the three intersection of the curve against the -axis of the graph. So, the smallest possible degree of the function is.

d.

  

Every polynomial is valid all over the real line. Let D stands for domain and R stands range, hence, the required domain and the range is:

Therefore, the solution for the given inequality is $\left\{x|x<-6\text{ or }x>-2\right\}$ .