Creating Polynomial Functions In Exercises 97100, find a polynomial function that has

Chapter 4, Problem 98

(choose chapter or problem)

Creating Polynomial Functions

In Exercises 97–100, find a polynomial function

\(f(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}\)

that has only the specified extrema.

(a) Determine the minimum degree of the function and give the criteria you used in determining the degree.

(b) Using the fact that the coordinates of the extrema are solution points of the function, and that the -coordinates are critical numbers, determine a system of linear equations whose solution yields the coefficients of the required function.

(c) Use a graphing utility to solve the system of equations and determine the function.

(d) Use a graphing utility to confirm your result graphically.

Relative minimum: (0,0); Relative maximum: (4,1000)

Equation Transcription:

Text Transcription:

f(x) = a_n x^n + a_n-1 x^n-1 + cdots + a_2 x^2 + a_1 x + a_0