×
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.3 - Problem 14e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.3 - Problem 14e

×

# Graphing polynomials Sketch a graph of the | Ch 4.3 - 14E

ISBN: 9780321570567 2

## Solution for problem 14E Chapter 4.3

Calculus: Early Transcendentals | 1st Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Calculus: Early Transcendentals | 1st Edition

4 5 1 261 Reviews
24
5
Problem 14E

9-14. Graphing polynomials Sketch a graph of the following polynomials. Identify local extrema, inflection points, and x- and y-intercepts when they exist.

$$f(x)=x^{3}-33 x^{2}+216 x-2$$

Step-by-Step Solution:
Step 1 of 3

Solution: Step1 Given that f(x)=x^3-33*x^2+216x-2 Differentiate the given equation to find f’(x) we get, f’(x)= 3*x^2-33*2*x+216 = 3*x^2-66x+216 Again differentiate f’(x) to find f’’(x) we get, f’’(x)=3*x^2-66x+216 = 3*2*x-66 =6x-66 Step2 To get extreme values we have to use f’(x)=0 => 3*x^2-66x+216=0 =>3(x^2-22x+72)=0 => x^2-22x+72=0 => x^2-4x-18x+72=0 =>x(x-4)-18(x-4)=0 =>(x-18)(x-4)=0 => x=18,4 Critical points are 4,18 Step3 To find inflection points we have to use f’’(x)=0 =>6x-66=0 =>6(x-11)=0 =>x-11=0 =>x=11 Evaluate f’’(x) at the critical points we get, f”(4 )=6x-66 = 6*4-66=24-66 =-42<0 has a local maximum at x=4 And f”(18)= 6x-66 = 6*18-66=108-66 =42>0 Has a local minimum at x=18 Step4 The corresponding function values are f(4 )=x^3-33*x^2+216x-2 = (4)^3-33*(4)^2+216*4-2 =64-33*16+864-2 =64-528+864-2 =928-530=398 and f(18 )= x^3-33*x^2+216x-2 = (18)^3-33*(18)^2+216*18-2 =5832-33*324+3888-2 = 5832-10692+3888-2 =-974 Finally we see that f”(x) changes sign at x=11 f(11)=-288 Therefore the inflection point is (11,-288) And the local maximum at (4,398) , Local minimum at (18,-974) For x-intercepts, we have to solve the equation f(x)=0 =>x^3-33*x^2+216x-2=0 Note :- Difficult to solve for x. I am getting complex value for x. Step5

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: polynomials, inflection, graph, graphing, identify. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 14E from 4.3 chapter was answered, more than 443 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 14E from chapter: 4.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “?9-14. Graphing polynomials Sketch a graph of the following polynomials. Identify local extrema, inflection points, and x- and y-intercepts when they exist.$$f(x)=x^{3}-33 x^{2}+216 x-2$$” is broken down into a number of easy to follow steps, and 24 words.

## Discover and learn what students are asking

Statistics: Informed Decisions Using Data : Discrete Probability Distributions
?State the conditions required for a Poisson process.

Statistics: Informed Decisions Using Data : Inference about the Difference between Two Medians: Independent Samples
?In Problems 1–8, use the Mann–Whitney test to test the given hypotheses at the = 0.05 level of significance. The independent samples were obtained ra

#### Related chapters

Unlock Textbook Solution