Tofind: the value of constant a and b of the curve given below.

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter 4, Problem 25RE
To determine

Tofind:the value of constant a and b of the curve given below.

Expert Solution

Thevalue of a=3 and b=7. respectively.

Explanation of Solution

Given:

y=x3+ax2+bx+1

Concept used:

Point of inflection is f(x)=0 .

Calculation:

y=x3+ax2+bx+1

At (1,6) equation will be:

6=13+a(1)2+b(1)+1 .

a+b=4 .

Point of inflection is f(x)=0 .

Since y=f(x)

f(x)=6x+2a=0

By putting the value of x=1 in the above equation:

6(1)+2a=0

a=3 .

Since a+b=4 ;

b=7.

Hence the value of a=3 and b=7. respectively.

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