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 55RE
To determine

Tofind:the function using its second derivative.

Expert Solution

Answer to Problem 55RE

Thefunction using its second derivative f(x)=x22-x3+4x4+2x+1.

Explanation of Solution

Given:

  f(x)=1-6x+48x2, f(0)=1, f(0)=2 .

Concept used:

Antiderivative=integration

  f(t)dt=f(t) . Or dydtdt=y .

Since, the multiplication of two operators ×ddt=1 .

Integration formula:

  xndx=xn+1n+1 .

  f(x)dx=f(x)dx=f(x) .

Calculation:

  f(x)=1-6x+48x2, f(0)=1, f(0)=2 .

  f(x)=1-6x+48x2 .

  f(x)dx=f(x)dx=f(x) .

  f(x)=(x-3x2+16x3+C)dx .

  f(x)=(x-3x2+16x3+C) .

  f(0)=2 .

  2=(0-3(0)2+16(0)3+C) .

  C=2.

  f(x)=(x-3x2+16x3+C) .

  f(x)=(x-3x2+16x3+2) .

  f(x)=(x-3x2+16x3+2)dx .

  f(x)=x22-x3+4x4+2x+C .

  f(0)=(0)22-(0)3+4(0)4+2(0)+C .

  C=1.

  f(x)=x22-x3+4x4+2x+1.

Hence the function using its second derivative f(x)=x22-x3+4x4+2x+1.

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