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Consider the following code: f[x_] := E^x; y[a_, 1/2 _] := f[a] + f'[a]*(x - 1/2); Manipulate[ Show[Plot[ {y[x, 1/2], f[x]}, {x, -2, 4}, {1/2, -2, 4}, PlotStyle -> {Thickness[0.003],...