BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 19P

a.

To determine

To write: The table whose sum is 19 and product is Maximum.

Expert Solution

Answer to Problem 19P

So according to the table only possible pairs whose sum is 19 and product is large (9,10)(10,9)

Explanation of Solution

Given information:

Table of number whose sum is 19 and product is Maximum.

Concept Used:

Let first number is x and second number is y. for maximum product x and y should be positive.

Calculation:

    X(first number)Y(second)Product
    11818
    21734
    31648
    41560
    51470
    61378
    71284
    81188
    91090
    10990

Conclusion:

The above values are the two numbers with product as large as possible.

b.

To determine

To Find: A function that shows the product as of one of two numbers.

Expert Solution

Explanation of Solution

Given information:

First number is x

Second number is y

Sum is 19

Product is Maximum

Concept used:

  x+y=19

  xy= Product................... 1

  x+y=19

  x=(19y)..................2

Put equation 2 in equation 1

Product =y(19y)

Product =19yy2

Conclusion:

The required function showing the product is 19yy2

c.

To determine

To Find: The solution by using your modal and compare the answer with subpart a.

Expert Solution

Explanation of Solution

Given information:

Two number whose sum is 19

  x+y=19xy= maximize

Concept used:

Maximize the product by using Differentiation

First differentiation is equal to 0 for maximize

Calculation:

Product =y(19y)

  p(y)=19yy2

Differentiate with respect to y

  p'(y)=192y

Put p'(y)=0 for maximum value

  192y=019=2yy=95

Then x=95

Conclusion:

From subpart (a) answer is (9,10) . Here x and y value is 95 . Because in subpart (a) only take the whole number that is why there is difference in the answer.

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