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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) Investigate the family of polynomials given by the equation f(x) = cx4 − 2x2 + 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 − x2. Illustrate by graphing this parabola and several members of the family.

(a)

To determine

To find: The value of c for the curve having minimum points.

Explanation

Given:

The function is f(x)=cx42x2+1

Calculation:

The function is as follows:

f(x)=cx42x2+1 (1)

Substitute 0 for c in equation (1).

f(x)=(0)x42x2+1=02x2+1=2x2+1 (2)

Sketch the graph for the function f(x)=cx42x2+1 for different values of c as shown below in Figure 1

(b)

To determine

To show: The minimum and maximum points of curves.

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