1/4.002 Use a linear approximation to estimate the given number. Can you review this for accuracy?

1/4.002    Use a linear approximation to estimate the given number. Can you review this for accuracy? If I've made an error please show every step of the correct answer. Here's what I have:

f(x) = 1/x= x-1                            

f'(x) = - 1/x2 

x = 4.002

a = 4

f(x) = f(a) + f'(a)(x - a)

L(4.002) = f(4) + (-1/42)(4.002 - 4)

                = 1/4 + (- 1/16)(0.002)

                = 1/4 - 0.000125

                = 0.249875

Thank you!