Question

Given: F(0)=3 and F'(0)=-2. What is the linear approximation for F(0.1)

Answer 1

Using the formula for linear approximations: \[f(x)\approx f(x_0)+f'(x_0)(x-x_0) \]We get:\[f(0.1)=f'(0)+f'(0)(0.1-0)\]You're given all the information you need to solve this :)

Answer 2

what about the F(0)=3

Answer 3

Sorry I had a typo:\[f(0.1)=f(0)+f'(0)(0.1-0)\]

Answer 4

Okay thank you

Answer 5

In case you want to check your answer:\[f(0.1)=3+(-2)(0.1-0)=2.8\]