A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three...

Question:

A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of a material that costs $4 per foot. The material for the fourth side costs $12 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.

Minimum of a Function

In the problem, we are asked for the dimension that makes the cost minimum. To get the value that makes a function minimum, find the first derivative of the function then equates it to zero. Solve the first derivative. The value that makes the first derivative zero is either a minimum or maximum. To check if its minimum, do a second derivative test and it should be equal to a positive number.

Answer and Explanation:

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Let's represent the dimensions as

{eq}length = x \\ width = y {/eq}

The area of a rectangle is computed by

{eq}A = length \times width \\ A =...

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Minimum Values: Definition & Concept

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Chapter 18 / Lesson 16
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The minimum value of a quadratic function is the low point at which the function graph has its vertex. This lesson will define minimum values and give some example problems for finding those values. A quiz will complete the lesson.


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