The discussion centers on the derivation of the second Taylor polynomial for the function f(x) = √x around the point a = 4. The user initially calculated the first and second derivatives but neglected to include the constant and linear terms in their polynomial expression. After receiving feedback, they recognized the omission of a negative sign and confirmed that including the constant term and linear term was necessary for the correct formulation of T₂. The final polynomial was verified as correct after these adjustments.
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What you have is the degree 2 term (almost). What's the sign?skyturnred said:Homework Statement
Here is the question:
I don't quite know what I did wrong. My method is below.
Homework Equations
The Attempt at a Solution
f(x)=√x
f'(x)=[itex]\frac{1}{2(x)^{1/2}}[/itex]
f''(x)=[itex]\frac{-1}{(2)(2)(x^{3/2}}[/itex]
a=4
f(a)=2
f'(a)=1/4
f''(a)=[itex]\frac{-1}{4(4^{3})^{1/2}}[/itex]
so wouldn't the second Taylor polynomial be what I put in the answer field above? Thanks.
SammyS said: