Fiesta 4
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AP CALCULUS AB | 2008 | Shubleka | Fiesta # 4
Name________________________
Please write your answers neatly on a separate sheet. No calculators are permissible on this assessment. 1. Show all your work for full credit. a. For what intervals is f ( x) = xe x concave up? b. For what intervals is f ( x) =
1 concave down? x +1 2
2. Find the quadratic polynomial g ( x) that best fits the function f ( x) = e x at x = 0 , in the sense that g (0) = f (0), and g '(0) = f '(0), and g "(0) = f "(0). 3. Determine the first and second derivative functions of f ( x) = x3 − 7 x + 6 . Where is the function twice-differentiable? Definition: A function is twice differentiable at a point if the second derivative exists at that point. A function is twice differentiable (in its domain) if it is twice differentiable at every point in the domain. [20 points]
Name________________________
Please write your answers neatly on a separate sheet. No calculators are permissible on this assessment. 1. Show all your work for full credit. a. For what intervals is f ( x) = xe x concave up? b. For what intervals is f ( x) =
1 concave down? x +1 2
2. Find the quadratic polynomial g ( x) that best fits the function f ( x) = e x at x = 0 , in the sense that g (0) = f (0), and g '(0) = f '(0), and g "(0) = f "(0). 3. Determine the first and second derivative functions of f ( x) = x3 − 7 x + 6 . Where is the function twice-differentiable? Definition: A function is twice differentiable at a point if the second derivative exists at that point. A function is twice differentiable (in its domain) if it is twice differentiable at every point in the domain. [20 points]
