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1. If f(x) = x-3 + 3 + 5π - e2, then f′(x) =
2. Find the absolute maximum of y = x3 - x2 - 7x on the interval [-2, 2].
3. Approximate the area under the curve y = x2 + 2 from x = 1 to x = 2 using four right-endpoint rectangles.
4. Approximate the area under the curve y = x2 + 2 from x = 1 to x = 2 using four inscribed trapezoids.
5. Evaluate .
6. Suppose . What is the change in f(x) as t increases from 1 to 4.
7. In the xy-plane, 2x + y = k is tangent to the graph of y = 2x2 - 8x + 14. What is the value of k ?
8. The function f is continuous on the closed interval [0,4] and twice differentiable over the open interval, (0, 4). If f′(x) < 0 and f″(x) > 0 over the interval (0, 4), which of the following could be a table of values for f ?