Fiesta 3
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AP CALCULUS AB | 2008 | Shubleka | Fiesta # 3
Name________________________
Please write your answers neatly on a separate sheet. No calculators are permissible on this assessment. 1. Draw the graph of a continuous function that satisfies the following conditions •
f '( x) > 0 x < −2
•
f '( x) < 0 − 2 < x < 2
•
f '( x) = 0 x > 2
[10 points]
2. Discuss the function f ( x) = x 3 − 7 x + 6 . Describe its continuity and differentiability in as much detail as possible. A function is differentiable at a point if the derivative exists at that point. A function is differentiable in its domain if it is differentiable at every point. [20 points]
3. Find the derivative function of f ( x) =
1 [20 points] x +1
Name________________________
Please write your answers neatly on a separate sheet. No calculators are permissible on this assessment. 1. Draw the graph of a continuous function that satisfies the following conditions •
f '( x) > 0 x < −2
•
f '( x) < 0 − 2 < x < 2
•
f '( x) = 0 x > 2
[10 points]
2. Discuss the function f ( x) = x 3 − 7 x + 6 . Describe its continuity and differentiability in as much detail as possible. A function is differentiable at a point if the derivative exists at that point. A function is differentiable in its domain if it is differentiable at every point. [20 points]
3. Find the derivative function of f ( x) =
1 [20 points] x +1
