My problem is . My answer was . My work is as follows f(x) = ln x

f'(x)= 1/x

55 appx = e^4 which is 54.6

f(e^4)= 4

f'(e^4)= 4/(e^4)

x-a=h= 55 - 54.6 = .4

f(55)= f(55+(55-54.6)) appx = f(e^4) + f'(e^4)*(55 - 54.6)

appx = 4 + 4/(e^4) (55-54.6) = 4 + (8/(e^4)) - 4 = 8/5(e^4)

When you type this in the calculator ln(55) = 4.007 and 8/(5(e^4)) = .029 which is not close at all. Can anyone explain to me what I'm doing wrong, or am missing?