Problem 1. For each statement below, indicate whether the statement is true or f

1. False (because if it has pick at c then it is not differentiable) 2. True 3. True 4. False 5. False 6. False

ID: 2843551 • Letter: P

Question

Problem 1. For each statement below, indicate whether the statement is true or

false. You do not need to justify your reasoning.

(1) True/False: If a function is continuous at x = a, it is dierentiable at

x = a.

(2) True/False: If a function has an inverse, it must be one-to-one.

(3) True/False: If f(x) has an inflection point at x = c, then f0(c) = 0.

(4) True/False: For f a dierentiable function, if f(x) is increasing on (a; b), then f0(c) < 0 for c in (a; b).

(5) True/False: All continuous functions are integrable.

(6) True/False: If a function is not continuous, it is not integrable.

1. False (because if it has pick at c then it is not differentiable)

2. True

3. True

4. False

5. False

6. False

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