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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

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Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Creating Polynomial Functions In Exercises 103-106, find a polynomial function

f ( x ) = a n x n + a n 1 x n 1 + + 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 detennining the degree, (b) Using the fact that the coordinates of the extrema are solution points of the function, and that the x-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: (1, 2); Relative maxima: (- 1,4), (3.4)

(a)

To determine
The minimum degree of a polynomial that would satisfy the provided conditions the function has a relative minimum at (1,2) and two relative maxima at (1,4),(3,4).

Explanation

Given:

The function has a relative minimum at (1,2) and two relative maxima at (1,4),(3,4)

(b)

To determine
A system of equations that can be used to identify the polynomial that would satisfy the provided conditions the function has a relative minimum at (1,2) and two relative maxima at (1,4),(3,4).

(c)

To determine

To calculate: The polynomial by solving of the provided system of equations in part b) using a graphing utility.

(d)

To determine

To graph: The polynomial obtained in part c) and to verify the relative extremas.

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