Linearization and approximation

Question

If f(1) = 5 and  , which of the following is the best approximation for f(1.03) using local linearization? 

Options:

1. 9.06
2. 5.06
3. -4.94
4. -5.97

Answer 1

slope M = fPrime(1) = 2

(1,5) is on the line.

B = y - mx = 5 - 2*1 = 3

y = 2x+3

for x = 1.03,

the line says, 2*1.03 + 3 = 2.06+3 = 5.06