   Chapter 10.4, Problem 2CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Suppose we want to find the minimum value of C   = 5 x   +   2 y and we know that x and y must be positive and that x y =   1000 .Find the critical values.

To determine

To calculate: The critical values of the equation C=5x+2y when x,y are positive and xy=1000.

Explanation

Given Information:

The equation is C=5x+2y when x,y are positive and xy=1000.

Formula used:

To find the critical value of an equation, differentiate the function with respect to the independent variable and equate it to 0. the relevant value is the critical value that satisfies the provided conditions.

The power rule is used for a function in which the expression can be written as every term raised to a power (be it fractional, positive or negative). For the function f(x)=xn, the derivative is

ddx[xn]=nxn1

Calculation:

Consider the provided equation:

C=5x+2y

Where x,y are positive and xy=1000

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