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Chapter 4: Q. 10 (page 241)

Solve the inequality by using the graph of the function.

Solve f(x)≤0, where

f(x)=x(x+2)2

Short Answer

Expert verified

The solution of the inequality is (-∞,0).

Step by step solution

01

Step 1. Given Information

We are given a function,

f(x)=x(x+2)2

02

Step 2. Graphing the function 

The graph of the function f(x)=x(x+2)2is as follows,

03

Step 3. Solve the inequality 

As seen from the graph, f(x)≤0for (-∞,0).

Hence the solution is(-∞,0).

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Most popular questions from this chapter

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=x5-x4+2x2+3

Solve the inequality algebraically.

x3+2x2-3x>0

In Problems 63–72, find the real solutions of each equation.

2x3+3x2+2x+3=0

Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.

In Problems 49– 60, for each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.

(c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x|

f(x)=3(x-7)(x+3)2
See all solutions

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