1. The graph of a differentiable function f on the closed interval [-3,15] is shown in the figure above. The graph of f has a horizontal tangent line at x = 6. Let g(x) = f(t)dt for −3 ≤ x ≤ 15. (a) Find g(6), g'(6), and g"(6). (b) On what intervals is g decreasing? Justify your answer. (c) On what intervals is the graph of g concave down? Justify your answer. 15 (d) Find a trapezoidal approximation of f¹5 f(t)dt using six subintervals of equal length At = 3.

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