BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 62RE
To determine

To explain: The various possible shape with help of graph.

Expert Solution

Explanation of Solution

Given information:

The equation is f(x)=x4+x3+cx2 .

Calculation:

Consider the equation.

  f(x)=x4+x3+cx2

Differentiate above equation.

  f(x)=4x3+3x2+2cx

Substitute f(x)=0 in above equation.

  4x3+3x2+2cx=0x(4x2+3x+2c)=0x=0,3±932c8

Differentiate above equation.

  f(x)=12x2+6x+2c

Substitute f(x) in above equation.

  12x2+6x+2c=0x=3±924c12

Since, the inflection point depends on discriminant.

  c=0,38

The graph is shown below.

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 62RE

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