Finding the Linearization of f(x): Find the linear approximation L\'(x) of the f

Question

Finding the Linearization of f(x): Find the linear approximation L'(x) of the function f(x) = x/root x+1 at x = 0. Use this linearization to approximate f(0.03).

1a) In Maple, create a text region and enter the following sentence: Question 1. Insert an execution group (command

prompt) after the the text region.

1b) In Maple, create the function f(x) = x/root x+1.

c) Using Maple, calculate f(0). ANSWER:______________________________

d) Using Maple, calculate f 0(x) and f 0(0) . ANSWER:______________________________________

e) What is L'(x)? (Determine this by hand.)

ANSWER:__________________________________________________________

f) Using your answer from part (e), enter L'(x) in Maple? (Note: Use

Explanation / Answer

Here's the algorithm you should follow: you have anf(x)and a givenx0=0; take the derivativef?(x), and evaluate it asm=f?(x0). Thisf?(x0)should be anumber, not a function ofx. The line you need isy=m(x?x0)+f(x0). Again,f(x0)is anumber, and not a function ofx.

I hope this helps

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