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
[Math] Find function ‘f’ with given tangent line and given point
calculus
Best Answer
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).