Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

System of linear equations wikipedia, lookup

System of polynomial equations wikipedia, lookup

Fundamental theorem of algebra wikipedia, lookup

Quadratic equation wikipedia, lookup

Elementary algebra wikipedia, lookup

Quartic function wikipedia, lookup

Cubic function wikipedia, lookup

Transcript

Chapter 3.7–4 Find two positive numbers whose product is 154 and whose sum is a minimum. Solution: Let the two points be represented by the symbols x and y . The phrase “two positive numbers whose product is 154” can be represented by the equation xy = 154 . This is the equation that shows the relationship between x and y . The phrase “whose sum is a minimum “ can be represented by the equation x + y = S , where S is a real number. This is the equation where we minimize the sum. From the equation xy = 154 , y = 154 154 . Substitute this value in the equation x + =S. x x Take the derivative, find the critical number(s), and test them. x+ 154 = x + 154 x −1 = S x S ' ( x ) = 1 − 154 x −2 = 0 x 2 = 154 x = ± 154 We delete the negative number because the problem stated positive numbers. Let’s test the critical number. S ' (150 ) = 1 − 154 ( 150 ) 2 < 0 . This means the function is decreasing to the left of the critical number. S ' (160 ) = 1 − 154 ( 160 ) 2 > 0 This means the function is increasing to the right of the critical number. This means that x = 154 is the location of a local minimum. The other number is y= 154 154 = = 154 . x 154 The two numbers are both 154 . The product of the numbers is 154 and the sum is 2 154 .