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# Class Note for MATH 1431 with Professor Caboussat at UH 2

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Date Created: 02/06/15
MATH 1431 19328 Alexandre Caboussat Lecture MWF 11AM 12PM Office hours MWF 12PM 1PM httpwwwmathuheduNcaboussatmath1431 I HWTH 1431 1 Chap 4 44 How to Find Absolute Extreme Values Suppose f is continuous on 37 b and differentiable on 37 b 0 Compute fa and fb 0 Compute fc for every critical number c in 37 b 0 Compare these values Find the absolute extreme values for the function fX 7X3 h le 6X7 3 on the interval 74700 0 Critical numbers X 72 X 3 0 Endpoints X 74 0 What happens when X a 00 METH 1411 Behavior when X gt ioo 7 fXgtOO aSXHOO fX becomes arbitrary large when X increases without bound fXgtOO aSXHOO fX becomes arbitrary large negative when X increases without bound Examples METH 1411 Behavior when X gt ioo 7 fXgtOO aSXHioo fX becomes arbitrary large when X decreases without bound fX H700 aSXH foo fX becomes arbitrary large negative when X decreases without bound Examples METH 1411 Polynomials 1 fx aan an71xrquot 31X 30 fxx4ix3xzxl fx 72xxQ fx 7x3 x2 100000x 71 fx X3 7 sinx Recipe extended 9 Compute the value of the functions at the endpoints if any 9 Compute the behavior of the function when x a ioo if needed 0 Compute fc for every critical number 6 in 37 b 0 Compare these values on the interval 17 oo Find the absolute extreme values for the function fXX22X1 on the interval 7007 O More Difficult Find the absolute extreme values for the function x1 flxxil on the interval 27 oo Of all the rectangles with a given diagonal of length 1 show that the square has the largest area Of all the rectangles with a given diagonal of length 1 show that the square has the largest area 45 MinMax Problems rmeH 1411 shape what is the best angle what is the best position etc We want to talk about optimization problems what is the best I We look for the minimummaximum of some function maximize the area maximize the perimeter maximize the volume etc A triangle is formed by the coordinates axis and a line going through the point 27 5 with negative slope m Question Determine the slope of this line such that the area of the triangle is minimum Let39s try A triangle is formed by the coordinates axis and a line going through the point 27 5 with negative slope m Question Determine the slope of this line such that the area of the triangle is minimum Strategy 0 Draw a representative figure and locate the relevant quantities on it Strategy 0 Draw a representative figure and locate the relevant quantities on it 0 Identify the quantity to be maximizedminimized and find the formula for this quantity Strategy 0 Draw a representative figure and locate the relevant quantities on it 0 Identify the quantity to be maximizedminimized and find the formula for this quantity 9 Express the quantity to be maxmin as a function of one variable only Use the given relations to do such simplifications Strategy 0 Draw a representative figure and locate the relevant quantities on it 0 Identify the quantity to be maximizedminimized and find the formula for this quantity 9 Express the quantity to be maxmin as a function of one variable only Use the given relations to do such simplifications 0 Determine the domain of the function Strategy 0 Draw a representative figure and locate the relevant quantities on it 0 Identify the quantity to be maximizedminimized and find the formula for this quantity 9 Express the quantity to be maxmin as a function of one variable only Use the given relations to do such simplifications 0 Determine the domain of the function 6 Find the extreme values critical numbers endpoints etc A string is 3 feet long We want to either form a square a circle or a square and a circle from the string so that the total area is maximized How should we proceed A string is 3 feet long We want to either form a square a circle or a square and a circle from the string so that the total area is maximized How should we proceed

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