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Welcome to Week 4 Lecture 10 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This lecture explores the idea of turning points in polynomial functions and their connection to the degree of the polynomial. Turning points are defined as places where the graph switches from increasing to decreasing, or vice versa. We investigate the hypothesis that a polynomial of degree n can have at most n–1 turning points, and examine examples that support this rule. The lecture also highlights the importance of turning points in sketching graphs and emphasizes the current limitations in proving such results without calculus. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, Visit:https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #PolynomialFunctions #TurningPoints #GraphingPolynomials #EndBehavior #ZerosOfPolynomials #XIntercepts #DegreeOfPolynomial #CubicFunctions #QuadraticFunctions #Math #Mathematics #Calculus #IncreasingFunctions #DecreasingFunctions #RootsOfPolynomials
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