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 2.6, Problem 22E
To determine

  a=2

To sketch:The graph of the function where values of function are given at some points.

Expert Solution

Answer to Problem 22E

Value of the function and derivative of the function at are 3 and 4 respectively.

Explanation of Solution

Given: y=g(x) and g(0)=g(2)=g(4)=0,

  g'(1)=g'(3)=0,g'(0)=g'(4)=1

  g'(2)=1,limxg(x)=, and limxg(x)=

Let g(x)=ax2+bx+c be any function.

It has to find the graph and equation of the function.

  g(x)=0 For x=0,2,4(given)

  g'(x)=0 For x=1,3

  g'(x)=1 For x=0,4 and g'(2)=1

Now

  g'(x)=16(x1)(x3)(6(x2)2)

Integrate with respect to x then g(x)

  g(x)=16(x1)(x3)(6(x2)2)dx=x530+x4317x318+x33+x

Graph of g(x)=x530+x4317x318+x33+x is given below

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.6, Problem 22E

Hence, the function is g(x)=x530+x4317x318+x33+x .

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