Question

Suppose that f(600) = 9000 and f' (600) = 20. Estimate each of the following.

(a) f(601)
(b) f(600.5)
(c) f(599)
(d)f(598)
(e) f(599.75)

Answer 1

Using the linear approximation formula, we can estimate the values of f(601), f(600.5), f(599), f(598), and f(599.75) based on the given information.

Step-by-step explanation:

To estimate each of the following values, we can use the concept of linear approximation. The linear approximation formula is given by: f(x) ≈ f(a) + f'(a)(x - a). Let's use this formula to estimate the values.

1. f(601) ≈ f(600) + f'(600)(601 - 600) = 9000 + 20(601 - 600) = 9020
2. f(600.5) ≈ f(600) + f'(600)(600.5 - 600) = 9000 + 20(600.5 - 600) = 9010
3. f(599) ≈ f(600) + f'(600)(599 - 600) = 9000 + 20(599 - 600) = 8980
4. f(598) ≈ f(600) + f'(600)(598 - 600) = 9000 + 20(598 - 600) = 8960
5. f(599.75) ≈ f(600) + f'(600)(599.75 - 600) = 9000 + 20(599.75 - 600) = 8995