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| 1. Let f be a differentiable odd function defined on R. (That is f(-x) = -f(x) for all x in R.) Let a be a positive number. How many solution(s) could the equation af'(x) = f(a) have? | |
| a) | 0 |
| b) | 1 |
| c) | 2 |
| d) | 3 |
| 2. Let f be a quadratic function defined on the interval [a,b] with 0 < a < b. Which one of the followings is the value of c in (a,b) such that f(b)-f(a) = f'(c)(b-a) ? | |
| a) | (a+b)/2 |
| b) | (ab)½ |
| c) | 2ab/(a+b) |
| d) | Cannot be determined |
| 3. The Mean Value Theorem is applied to the function f(x) = x3 + qx2 + 5x - 6 on the interval [0,2]. Suppose that the number c determined by the theorem is equal to 2. Which one of the followings is the value of q ? | |
| a) | -1 |
| b) | -2 |
| c) | -3 |
| d) | -4 |
4. Which of the following functions satisfy the
conditions of the Mean value Theorem on their domains ?
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| a) | (I) and (III) | ||||||||||||
| b) | (I) and (IV) | ||||||||||||
| c) | (II) and (III) | ||||||||||||
| d) | (II) and (IV) | ||||||||||||