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# Calculus I MATH 201

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This 2 page Class Notes was uploaded by Ms. Shyann Nader on Saturday October 3, 2015. The Class Notes belongs to MATH 201 at Bucknell University taught by Staff in Fall. Since its upload, it has received 8 views. For similar materials see /class/218085/math-201-bucknell-university in Mathematics (M) at Bucknell University.

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Date Created: 10/03/15

Math 201 Applied Optimization 46 Day 44 To optimize quantities in real world situations we can follow the steps below i Determine what quantity you want to optimize and give it a name call it y for now 11 Write y as a function of other quantities in the problem Use other information in the problem to re write y as a function of only one variable iv Find all local extrema of y V Find the behavior of y near the edges of the domain On a closed interval 11 this means nding the value of y at a and b On an open interval a 1 this means nding the limit of y as it approaches a and b In the open interval a and I could be ioo vi Compare the y values from the previous two parts to determine absolute extrema if they exist vii Interpret your answer and state a solution to the problem given Use these steps to solve the following problems 1 The legs of a right triangle not including the hypotenuse have a total length of 12 What is the maximum area that this triangle could have 2 The United States Postal Service considers a rectangular package oversized if the sum of the length width and height is more than 108 inches If the length is twice the width what is the largest volume that a package can be without being oversized What are the dimensions of the box A DJ V Speedy the mouse can run 8mph and swim 2mph Speedy wants to cross a river that is 110 of a mile wide and end up 15 mile downstream lf Speedy swims in a diagonal line across the river and then runs down the river bank what is the minimum amount of time that it could take Speedy to get to the destination How far will Speedy swim How far will Speedy run What is the total distance Speedy will travel 15 Math 201 Computlng Derlvatlves Name Compute the following derivatives You may use the shortcuts unless otherwise indicated 1 Use the limit de nition to compute the derivative of fz 31 lt2 gltzgt3 3 hz 351 tanz 7 arctanz 91nz 4 cm tanz 5 m 527139m lt6 mltz 7 Does this match with the rule I gave you 8 PM 1 4901000 lt9 qltzgt ea 10 rm 551mm 11 3m lnm7 12 tz sec2m 13 1n52m 14 vz 6m arctan13z2 15 495 nigh 16 sincos1n9m 1 at m 1 2 at m Z 3 rm at m 4 at m i 20 5 11m at m 7 i

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