# The average rate of change of C with respect to x when the production level is changed from from x = 100 to x = 105 . ### 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 2.6, Problem 45E

i.

To determine

## The average rate of change of C with respect to x when the production level is changed from from x=100 to x=105 .

Expert Solution

### Explanation of Solution

Given information:

The cost (in dollars) of production of x units of a certain commodity is

C(x)=5000+10x+0.5x2

Calculations:

Here the cost of producing 100 unit  is

C(100)=5000+10×100+0.5×1002C(100)=5000+1000+5000=11000

Here the cost of producing 101 unit  is

C(101)=5000+10×101+0.5×1012=11110.5

Here the cost of producing 102 unit  is

C(102)=5000+10×102+0.5×1022=11222

Here the cost of producing 103 unit  is

C(103)=5000+10×103+0.5×1032=11334.5

Here the cost of producing 104 unit  is

C(104)=5000+10×104+0.5×1042=11448

Here the cost of producing 105 unit  is

C(105)=5000+10×105+0.5×1052=11562.5

Now, Rate of change of production cost from x=100 to x=101 is 11110.511000=110.5

Rate of change of production cost from x=101 to x=102 is 1122211110.5=111.5

Rate of change of production cost from x=102 to x=103 is 11334.511222=112.5

Rate of change of production cost from x=103 to x=104 is 1144811334.5=113.5

Rate of change of production cost from x=104 to x=105 is 11562.511448=114.5

Now the average rate of change of production cost(C) from x=100 to x=105 is 110.5+111.5+112.5+113.5+114.55=562.55=112.5

ii.

To determine

Expert Solution

### Explanation of Solution

Given information:

The cost (in dollars) of production of x units of a certain commodity is

C(x)=5000+10x+0.5x2

Calculations:

Here ,The cost of producing 100 unit  is

C(100)=5000+10×100+0.5×1002C(100)=5000+1000+5000=11000

The cost of producing 101 unit  is

C(101)=5000+10×101+0.5×1012=11110.5

Now,

Rate of change of production cost from x=100 to x=101 is 11110.511000=110.5

iii.

To determine

Expert Solution

### Explanation of Solution

Given information:

The cost (in dollars) of production of x units of a certain commodity is

C(x)=5000+10x+0.5x2

Calculations:

Here, the cost of producing 100 unit  is,

C(100)=5000+10×100+0.5×1002C(100)=5000+1000+5000=11000

Here the cost of producing 99 unit  is

C(99)=5000+10×99+0.5×992=10890.5

Now,

The instantaneous rate of change of C with respect to x when x=100  is 1100010890.5=109.5

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