SCRiBE =)

Hello! I'm known as Tim-Math-Y and I will be the scribe for today's lessons! Today, Mr.Kuropatwa was victim to a fourth computer crash and thus lost most of his data, including that of today's lesson! However, Mr.Kuropatwa is quite the resourceful teacher and came up with problems for us to place our minds into. We were separated into work groups in which we aided each other in solving optimization problems, a continuation.

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SLIDE1:
-the first step, which is nearly undeniable as the most important step in solving these types of problems, is picturing the problem, most commonly through a drawn diagram of the situation
-second, we set up variables and expressions for the unknown distances of the diagram
-third, referring to the rate-distance-time triangle on slide 3, we set up a a function where X is a function of Time (the time taken to travel in water + the time taken to travel via walking)
-fourth, we find the first derivative of the function using chain rule and power rule, then simplify using LCD (Lowest Common Denominator)
-fifth, we find the roots of the first derivative in order to locate where possible mins or maxes may occur. In this situation, we are looking for a possible minimum. Roots are located at +/- 3/2.

SLIDE2:
-first, we depict a number line of T'(X), displaying the two possible mins or maxes
-second, we use the first derivative test to identify whether the extrema are mins or maxes and discover what we hope to attain: a minimum

SLIDE3:
-Simply put, we imputted the minimum value of 3/2 into the parent function T(X) to find the minimal amount of time in hours to complete the trip

Afterwards, we were handed a worksheet to work in our separate groups. It was not required to be handed in today.

Question:

Scuba Steve's Shark Cages

Scuba Steve is enclosing an area of his harbor for two sharks that we wants to keep as pets (Don't try this at home). He has 450 ft. of fencing for the sides of two cages. He needs to separate the two so they won't kill each other, but they need to have the same sized cages. What is the maximum area of each section of the cage that he can build?

If you haven't already solved this problem, here are some guidelines to follow:
-draw a labelled diagram
-apply variables (there will be 3 widths, and 2 lengths)
-find a function relating to area (length x width)
-find the first derivative
-find the roots of the derivative
-run the first derivative test to identify whether it is a min/max
-substitute your minimum x value into the parent function to find the max area
-top it off with a sentence solution

Answer: 4218.75 ft^2

And that, ladies and gents is today's scribe.

Thursday's scribe will be... Phuong? It has a (-) beside your name on the scribe list ... sorry! =)

Adieu, adieu.. adieu!

... Quod Erat Demonstrandum - And Thus it is Proven