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 1.1, Problem 23E
To determine

To find: the solution for the given function.

Expert Solution

Explanation of Solution

Given information:

The given function is,

  f(x)=3x2x+2

Concept used:

To represent the function:

A function f is a rule that assigns to each element x in a set D exactly one element called f(x) in a set E

The given function is

  f(x)=3x2x+2

Calculate f(2) as,

  f(2)=3(2)22+2=3×4=12

And f(2)=16

Calculate the all difference quotient for x in the given function f(x)=3x2x+2 ,

Then,

  f(a)=3(a)2a+2=3a2a+2

  f(a)=3(a)2(a)+2=3a2+a+2

And 2f(a)=2(3a2a+2)=6a22a+4

Now, solved for the function f(x)=3x2x+2 as,

  f(a+1)=3(a+1)2(a+1)+2=3(a2+1+2a)a1+2=3a2+3+6aa+1=3a2+5a+4

  f(2a)=3(2a)22a+2=12a22a+2=2[6a2a+1]

And,

  f(a2)=3(a2)2a2+2=3a4a2+2

Now,

  [f(a)]2=[3a2a+2]2=[(3a2)2+a2+42×3a2×a2×a×2+2×3a2×2]=[9a4+a2+46a34a+12a2]=[9a46a3+13a24a+4]

Thevaluesof f(a+h) for the function f(x)=3x2x+2 is simplify as,

  f(a+h)=3(a+h)2(a+h)+2=3(a2+h2+2ah)ah+2=3a2+3h2+6ahah+2

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