Approximation of Local Linearization

Question

If f(2) = 10 and  , which of the following is the best approximation for f(2.03) using local linearization?

a) 10.03

b) -7.97

c) 3.03

d)8.03

Answer 1

For a particular value a, if you know f(a) and f '(a), then, for small values h, f(a + h) is approximately

f(a) + f '(a) * h.

Here a = 2, and h = 0.03.