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find the function 'f' whose tangent line has slope (x+2)e^(-4x) +4 and whose graph passes through (0,1).

I have tried doing the derivative and plugging in x but it is not working

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you need to integrate t(x) = (x+4)e^(-4x) + 4 to get f(x). When you integrate t(x) you will have a constant term but you can find the value of the constant as the graph of f passes through (0,1) i.e. f(0) =1.

When you differentiate f(x) you get t(x) which is the tangent to f(x).

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