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Question
i'm having trouble with this kind of problem
Find all extrema in the interval [0,2π] if y= x + cos x
i thought the answer is (3π/2,3π/2) but it isn't
:))

Answer
Remember , the extreme values don't necessarily occur where the derivative is 0 . The extreme values occur where the derivative is 0 or at the endpoints.


y' = 1 - sin(x)



since sin(x)< = 1 , y' is non negative and the function is non decreasing.

Thus , the extreme values occur at the endpoints of the interval . The minimum is 1 when x = 0 , maximum is 2π + 1 when x = 2π

Calculus

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I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

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