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!