设f(x)f(x)f(x)在[a,b][a,b][a,b]上满足f(x)>0,f′(x)<0,f′′(x)>0f(x)>0,f'(x)<0,f''(x)>0f(x)>0,f′(x)<0,f′′(x)>0,其中0<a<b0 < a < b0<a<b,令S1=∫abf(x)dx,S2=f(b)(b−a),S3=12(f(b)+f(a))(b−a)S_1=\int_{a}^{b} f(x)dx,S_2 = f(b)(b - a),S_3=\dfrac{1}{2}(f(b)+f(a))(b - a)S1=∫abf(x)dx,S2=f(b)(b−a),S3=21(f(b)+f(a))(b−a),则S1,S2,S3S_1,S_2,S_3S1,S2,S3的大小顺序为( ).
(A)S2<S1<S3S_2 < S_1 < S_3S2<S1<S3
(B)S1<S2<S3S_1 < S_2 < S_3S1<S2<S3
(C)S3<S1<S2S_3 < S_1 < S_2S3<S1<S2
(D)S1<S3<S2S_1 < S_3 < S_2S1<S3<S2
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