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\begin{aligned} &A(1)=1, A(2)=1.5, A(3)=1, A(4)=0.5 \\ &A^{\prime}(x)=f(x) \text { so } A^{\prime}(1)=f(1)=1, A^{\prime}(2)=f(2)=0, A^{\prime}(3)=-1, A^{\prime}(4)=0 \end{aligned}