Homework Help is Here – Start Your Trial Now!
Math
Algebra
Given the function C(t) = -2t6 +t¹2+tº+t There are at most at most x-intercepts, and turning points.

Given the function C(t) = -2t6 +t¹2+tº+t There are at most at most x-intercepts, and turning points.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 7E
See similar textbooks
icon
Related questions
Question
### Polynomial Function Analysis Given the polynomial function \( C(t) = -2t^6 + t^{12} + t^9 + t \): 1. **Number of x-intercepts:** There are at most \(\_\_\_\_\_\_\_\) x-intercepts. 2. **Number of turning points:** There are at most \(\_\_\_\_\_\_\_\) turning points. In analyzing the given function, the maximum possible x-intercepts and turning points can be deduced from its degree. The degree of the polynomial function \( C(t) \) is determined by the highest power of \( t \), which in this case is 12 (i.e., \( t^{12} \)). - **X-Intercepts:** A polynomial of degree \( n \) can have at most \( n \) x-intercepts. Therefore, the function \( C(t) \) can have at most 12 x-intercepts. - **Turning Points:** A polynomial of degree \( n \) can have at most \( n-1 \) turning points. Therefore, the function \( C(t) \) can have at most \( 12-1 = 11 \) turning points.
Transcribed Image Text:### Polynomial Function Analysis Given the polynomial function \( C(t) = -2t^6 + t^{12} + t^9 + t \): 1. **Number of x-intercepts:** There are at most \(\_\_\_\_\_\_\_\) x-intercepts. 2. **Number of turning points:** There are at most \(\_\_\_\_\_\_\_\) turning points. In analyzing the given function, the maximum possible x-intercepts and turning points can be deduced from its degree. The degree of the polynomial function \( C(t) \) is determined by the highest power of \( t \), which in this case is 12 (i.e., \( t^{12} \)). - **X-Intercepts:** A polynomial of degree \( n \) can have at most \( n \) x-intercepts. Therefore, the function \( C(t) \) can have at most 12 x-intercepts. - **Turning Points:** A polynomial of degree \( n \) can have at most \( n-1 \) turning points. Therefore, the function \( C(t) \) can have at most \( 12-1 = 11 \) turning points.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS