   Chapter 3.6, Problem 27E

Chapter
Section
Textbook Problem

# (a) Investigate the family of polynomials given by the equation f ( x ) = c x 4 − 2 x 2 + 1 . For what values of c does the curve have minimum points?(b) Show that the minimum and maximum points of every curve in the family lie on the parabola y = 1 − x 2 . Illustrate by graphing this parabola and several members of the family.

To determine

a)

To investigate:

The family of polynomials given by the function fx=cx4-2x2+1 and the find value of c for which the curve has minimum points.

Explanation

1) Concept:

From the graph identify the minimum values

2) Given:

fx=cx4-2x2+1

3) Calculation:

We have, fx=cx4-2x2+1

Draw graph of f(x) for different values of c

To determine

b)

To show:

The minimum and maximum points of every curve in the family lie on the parabola y=1-x2

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