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1. Let G(x) = [f (x)]2. At x = a, the graph of f is increasing and concave downward, while G is decreasing. Which describes the graph of G at x = a ?
2. The value of c for which has a local minimum at x = 3 is
3. An object moving along a line has velocity v (t) = t cos t - ln (t + 2), where 0 ≤ t ≤ 10. The object achieves its maximum speed when t is approximately
The graph of f ′, which consists of a quarter-circle and two line segments, is shown above. At x = 2, which of the following statements is true?
5. Let where f is the function whose graph appears below.
The local linearization of H(x) near x = 3 is H(x)
6. The table shows the speed of an object, in feet per second, at various times duringa 12-second interval.
Estimate the distance the object travels, using the midpoint method with 3 subintervals.
7. In a marathon, when the winner crosses the finish line many runners are still onthe course, some quite far behind. If the density of runners x miles from the finish line is given by R(x) = 20[1 - cos(1 + 0.03x2)] runners per mile, how many are within 8 miles of the finish line?
8. Which best describes the behavior of the function at x = 1?
9. If then f ′(t) equals