2012年AP微积分BC简答题真题+答案+PDF下载
1. The temperature of water in a tub at time t is modeled by a strictly increasing, twice-differentiable function W,where W(t) is measured in degrees Fahrenheit and t is measured in minutes. At time t=0, the temperature of the water is 55°F. The water is heated for 30 minutes, beginning at time t=0. Values of W(t) at selected times t for the first 20 minutes are given in the table above.
(a) Use the data in the table to estimate W'12. Show the computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem.
(b) Use the data in the table to evaluate ∫200W'(t)dt. Using correct units, interpret the meaning of ∫200W'(t)dt in the context of this problem.
(c) For 0≤t≤20, the average temperature of the water in the tub is 1/20∫200W(t)dt.Use a left Riemann sum with the four subintervals indicated by the data in the table to approximate 1/20∫200W(t)dt.Does this approximation overestimate or underestimate the average temperature of the water over these 20 minutes?Explain your reasoning.
(d) For 20≤t≤25, the function W that models the water temperature has first derivative given by W'(t)=0.4√t cos（0.06t）. Based on the model, what is the temperature of the water at time t=25 ?
3. Let f be the continuous function defined on [-4, 3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x)=∫x1f(t)dt.
(a) Find the values of g(2) and g(-2).
(b) For each of g'(-3) and g''(-3), find the value or state that it does not exist.
(c) Find the x-coordinate of each point at which the graph of g has a horizontal tangent line. For each of these points, determine whether g has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers.
(d) For -4＜x＜3, find all values of x for which the graph of g has a point of inflection. Explain your reasoning.
2012年AP微积分BC简答题真题余下省略！
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