Suppose #T_4(x) = 7-3(x-2)+7(x-2)^2-6(x-2)^2+8(x-2)^4# is the degree 4 Taylor polynomial centered at x=2 for some function f, how do you estimate the value of f'(1.9)?
Deeper 2 4 7 X 6
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1 Answer
Depending on the final details in your approximation method, you could either say #f'(1.9) approx -4.612# (more accurate) or #f'(1.9) approx -4.4# (less accurate).
Explanation:
We have
Deeper 2 4 7 X 6
Therefore,
Deeper 2 4 7 X 6 Intercepts
Deeper 2 4 7 X 6 Y 4 7 X 6
Plague inc web game. To get the more accurate approximation, plug #x=1.9# into this last equation:
To get a less accurate approximation, we can get a linear approximation to #T_{4}'(x)# itself as #T_{4}'(x) approx -3+14(x-2)# . Then #f'(1.9) approx T_{4}'(1.9) approx -3+14*(-.1)=-4.4# .