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Week 6 of Lecture Notes

by: Monica Weisenbach

Week 6 of Lecture Notes MATH127

Monica Weisenbach
GPA 3.819
Calculus I for Life and Social Science Majors
Thurlow Cook

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About this Document

This is Week 6 of Lecture Notes for Calculus 127. It covers the quotient rule, maximums, minimums, inflection points and the derivatives of sin(x) and cos(x).
Calculus I for Life and Social Science Majors
Thurlow Cook
Class Notes
UMass, amherst, Umass Amherst, Calculus, 127
25 ?




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This 3 page Class Notes was uploaded by Monica Weisenbach on Thursday March 12, 2015. The Class Notes belongs to MATH127 at University of Massachusetts taught by Thurlow Cook in Spring2015. Since its upload, it has received 69 views. For similar materials see Calculus I for Life and Social Science Majors in Mathematics (M) at University of Massachusetts.

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Date Created: 03/12/15
Week 6 Lecture Notes Quotient Rule The quotient rule is fgx f g fg g2 In other words the derivative of fX divided by gX is the derivative of ftimes the function 9 minus function ftimes the derivative of 9 all over function g squared gm 7quot l 139 quot39 W1 llnx x2 Example Maximums Minimums and Inflection Points Maximums are high points of a function The global maximum is the highest point in the entire function while local maximums are high points of a certain stretch Minimums are low points of a function The global minimum is the lowest point in the entire function while local minimums are low points of a certain stretch Inflection points are points at which the graph changes concavity These points can be found easily using derivatives Mins and maxes show up as the roots of the first derivative Inflection points show up as the roots of the second derivative Example function Q1OOte5t First derivative more O001 S 5equotquot ICD 5 56 Ioo IS Second derivative Q39 oe39 quotlSt oquot IOOS I5 equot s IOOQKQ NUSQ 506quotquot 1 3 Graph of function Q The roots of Q are x2 critical point The roots of Q are x4 inflection point 75quot It s a little hard to see but the graph corroborates what was found 50quot 25quot Sinx and Cosx Sinx and oosx are derived from angles with circles Sinx oppositehypotenuse Cosx adjacenthypotenuse The derivative of sinx oosx the derivative of oosx sinx Question What is the equation of the tangent line at sinx at x2rt equation is either ymxb or yyomxxo sin2rt0 so 2110 yO m x2rt m f xo derivative of sinx oosx and oos2rt1 So yO1x2rt yx2rt Proof of why the derivative of sinx oosx KM 9 k D 39 S39n L vt r l I Is shims A9 Sine J 39 39 i Cosxe E e 9 5N9 2 5 n9


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