Find the linearization of the function f(x)=1/2x+1 at x=−1.

Question

Find the linearization of the function f(x)=1/2x+1 at x=−1.

Find the true values of f(x) and the approximations using L(x) below. Round all of your answers to 3 decimal places. You can use a calculator, spreadsheet, browser, etc. to calculate the exact values.

x the exact value of f(x) The approximate value L(x)

-1.1 [needed] [needed]

-1.01 [needed] [needed]

-1.001 [needed] [needed]

Answer 1

Is ithe function F(x) = 1/2x + 1 or 1/(2x+1)?

Either way the linearization is L(x) = f(-1) + f'(-1)(x+1)

You need to find the derivative. Evaluate f(x) and f'(x) at x = -1. Sub into the formula the value of (x+1) that you want to put in the table in order to get L(x). Obviously, f(x) is just plugging x into the function to see how good the linearization is.