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test1 rev

test1 rev - Math 136 Review problems for test 1 I will have...

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Math 136, Review problems for test 1 I will have office hours 1:30-2:30 on Thursday. We will have a review session at 3:30 on Friday, February 8, and I think it will be in BP 2. The test will be on Monday, February 11, 12:00-1:20 in the Terrace Room. The test will cover sections 6.1 to 6.7 and 7.1-2. You should know how to calculate a derivative from the definition and also using theorems. You could be asked to quote and/or to use the Chain Rule, Product Rule, Mean Value Theorem on domains in R n , Inverse Function Theorem, Implicit Function Theorem. You could be asked to prove some basic properties of the derivative and theorems that follow from the results you have learned. In particular, you could be asked to prove The local Lipschitz property for differentiable functions (Prop. 6.3.1) D ( f + g ) = D f + D g when f and g are differentiable D ( cf ) = c D f when f is differentiable and c R The n - dimensional Mean Value Theorem (Theorem 6.7.1) Parts of the proof of the Inverse Function Theorem for A R and f : A

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