types of functions

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The document discusses how to determine if a function is increasing or decreasing based on the derivative. It states that a function is increasing if the derivative is greater than 0, meaning lower x values map to lower y values. A function is decreasing if the derivative is less than 0, so lower x values map to higher y values. It then gives examples of increasing and decreasing functions based on their derivatives and identifies points where the derivative is 0 as critical points.

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 Y=F(X) IS INCREASING IF F’(X) >0
X<Y THEN F(X) < F(Y)

 Y=F(X) IS DECREASING IF F’(X)<0
 X<Y THEN F(X) > F(Y)

 1. Y=2X THEN Y’=2>0
 2. Y=4X+3 THEN Y’=4 >0

 IF Y= -2X THEN Y’= -2
 IF Y= -8X-3 THEN Y’= -8

 POINTS AT WHICH Y’=0 ARE CRITICAL POINTS

Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg Dear Dr. Kornbluth and Mr. Gorenberg, The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation. This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or unwillingness to rectify this violation through action requires accountability. Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots. The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee. • The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act. • The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X. • The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202

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