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Chapter 4: Q. 66 (page 242)

In Problems 63鈥�66, (a) graph each function by hand, and (b) solve f(x)鈮�0.

f(x)=x3-6x2+9x-4x2+x-20

Short Answer

Expert verified

Part a. The graph of the function is

Part b. The solution off(x)鈮�0is-5<x<鈭�.

Step by step solution

01

Part (a) Step 1. Given Information 

The given function isf(x)=x3-6x2+9x-4x2+x-20

We have to graph the function.

02

Part (a) Step 2. Sketch the graph of the function 

The graph of the function is

03

Part (b) Step 1. Given Information

The given function is f(x)=x3-6x2+9x-4x2+x-20

We have to solve forf(x)鈮�0

04

Part (b) Step 2. Solving for f(x)≥0

So First, case:

x3-6x2+9x-4x2+x-20鈮�0x3-6x2+9x-4鈮�0andx2+x-20>0x-12x-4鈮�0x-4x+5>0x鈮�4x>4andx<-5[Commonsolution]x>4

Second case:

x3-6x2+9x-4x2+x-20鈮�0x3-6x2+9x-4鈮�0andx2+x-20>0x-12x-4鈮�0x-4x+5>0x<4-5<x<4[Commonsolution]-5<x<4

So, the solution is-5<x<鈭�.

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Most popular questions from this chapter

In Problems 21鈥�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)=2x5-x4-x2+1

Solve the given inequality algebraically.

x+1x-1>0

Find the real zeros of f. Use the real zeros to factor f.

f(x)=x3-8x2+17x-6

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 39鈥�56, find the real zeros of f. Use the real zeros to factor f.

f(x)=2x4-3x3-21x2-2x+24
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