Finding the Linearization of f(x): Find the linear approximation Lo(x) of the fu

Question

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

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

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

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

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

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

ANSWER:

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

Explanation / Answer

Yes, you did it wrong. Probably because you keep confusing the independent variable in the tangent line with the independent variable of your function. Here's the algorithm you should follow: you have an f(x) and a given x0=0; take the derivative f?(x), and evaluate it as m=f?(x0). This f?(x0) should be a number, not a function of x. The line you need is y=m(x?x0)+f(x0). Again, f(x0) is a number, and not a function of x

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