Math Teacher Solving his own Calculus Exam

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Today we take a look at my test on applications of differential and integral calculus, which includes maximization and extremal value problems, reconstruction of functions and also some physics and area interpretations. Can I solve it myself, what are the challenges? Let's find out! =D

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0:00 Intro
1:07 Exam Outline & Information
6:16 Exercise 1 Maximizing a Cylinder
12:19 Exercise 2 Reconstructing a Polynomial
21:26 Exercise 3 Application of Integrals
27:00 Part B Solids of Revolution
31:54 Part C & D Densities and Approximations