Ok we're doing optimization, i don't understand why you have to derive, it just doesn't come naturally to me, like it's not something i instinctively think of doing...(adsbygoogle = window.adsbygoogle || []).push({});

My example

A company wants to fence a rectangular piece of land that is bordered on one side by a road and by a river on the opposite side. There will be no fence along the river. The fence along the road costs $3 per foot and the fence along the other two sites costs $2 per foot. If the rectangular piece of land must have an area of 10800 square feet, find the dimensions that will give the minimum cost. What is the minimum cost?

I understand the need to use 2 equasions like in related rates to help reduce, in this case, the number of variables in the cost function.

Eq#1: Min C = 3x + 4y

Eq#2: xy = 10800

y = 10800/x

Min C = 3x + 4(10800/x)

Min C = 3x + 43200/x [x > 0]

At this point... he derives, but why?

C' = 3 - 43200/(x^2)

Now he finds the critical numbers, why? And also, how can you just take the right side of the equasion of C' to do that?

CN: 3 = 43200/(x^2)

3x^2 = 43200

x^2 = 14400

x = 120

Now he finds the second derivitive, again, why?

C'' = 86400/(x^3)

C(120) > 0 => x = 120 will give Min C

Ans: x = 120, y = 90, Min C = $720

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# Little clarifier

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