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 56RE
To determine

Tofind:the function using its second derivative.

Expert Solution

Answer to Problem 56RE

Thefunction using its second derivative f(x)=x510+x442x33+5x224.1833x+2.

Explanation of Solution

Given:

  f(x)=2x3+3x2-4x+5, f(0)=2, f(1)=0 .

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)=2x3+3x2-4x+5, f(0)=2, f(1)=0 .

  f(x)=2x3+3x2-4x+5 .

  f(x)dx=f(x)dx=f(x) .

  f(x)=(x42+x32x2+5x+C1)dx .

  f(x)=(x42+x32x2+5x+C) .

  f(x)=(x42+x32x2+5x+C1)dx .

  f(x)=x510+x442x33+5x22+C1x+C2

  f(0)=(0)510+(0)442(0)33+5(0)22+C1(0)+C2 .

  C2=2.

  f(1)=(1)510+(1)442(1)33+5(1)22+C1(1)+C2 .

  f(1)=(1)510+(1)442(1)33+5(1)22+C1(1)+2

  0=4.1833+C1(1) .

  C1=-4.1833 .

  f(x)=x510+x442x33+5x224.1833x+2.

Hence the function using its second derivative f(x)=x510+x442x33+5x224.1833x+2.

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