Thursday

November 27, 2014

November 27, 2014

Posted by **Sunny** on Thursday, May 24, 2012 at 1:31am.

- Calculus -
**Bosnian**, Thursday, May 24, 2012 at 2:42ama = first number

b = second number

a * b = 48 Divide both sides by a

b = 48 / a

S = the sum of one of the numbers and the cube of the other number

S = a + b ^ 3

S = a + ( 48 / a ) ^ 3

S = a + 110,592 / a ^ 3

S = a + 110,592 * a ^ - 3

First derivaton :

d S / d a = 1 - 3 * 110,592 * a ^ - 4

d S / d a = 1 - 331,776 / a ^ 4

Second derivation :

d ^ 2 S / d a ^ 2 = - 3 * 331,776 ( - 4 ) * a ^ - 5

d ^ 2 S / d a ^ 2 = 1,327,104 / a ^ 5

A function has minimum or maximum in poit where first derivation = 0

If second derivaton < 0 function has maximum.

If second derivaton > 0 function has minimum.

In this case:

d S / d a = 1 - 331,776 / a ^ 4 = 0

1 = 331,776 / a ^ 4 Multiply both sides by a ^ 4

a ^ 4 = 331,776

a = fourth root of 331,776

a = + OR - 24

For a = - 24

d ^ 2 S / d a ^ 2 = 1,327,104 / a ^ 5 =

1,327,104 / - 7,962,624 = - -0.166667 < 0

function has maxsimum.

For a = 24

d ^ 2 S / d a ^ 2 = 1,327,104 / a ^ 5 =

1,327,104 / -7,962,624 = 0.166667 > 0

function has minimum.

So a = 24

b = 48 / a = 48 / 24 = 2

The mumbers are a = 24 and b = 2

Local minimum = a + b ^ 3 = 24 + 2 ^ 3 = 24 + 8 = 32

- Calculus -
**Sunny**, Thursday, May 24, 2012 at 4:27amThank you!!!

**Answer this Question**

**Related Questions**

pre-calculus - THe sume of 2 positive numbers is 20. Find the two numbers such ...

calculus - The sum of two positive numbers is 100. Let one of the numbers be x ...

math URGENT!!!! - i have a list of 5 different numbers. the sum of 2 of the ...

statistics - 400 draws are made at random with replacement from 5 tickets that ...

math - The sum of two positive numbers is 90. Find a function that models their ...

Math - Two numbers have a product of 3 1/5 and a sum of 3 3/5. One of the ...

math 5th grade - two numbers have a product of 3 1/5 and a sum of 3 3/5. One of ...

math - the product of two positive numbers is 9 18/25 and one of them is three ...

Math PLEASE HELP ASAP - -PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT ...

Pre-Calculus - Three numbers whose sum is 15 are in an arithmetic progression. ...