Suppose #T_4(x) = 7-3(x-2)+7(x-2)^2-6(x-2)^3+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(2.1)?

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Answer 1 · 2016-10-08T13:00:53

#6.7#

#T_4(2) = 7# and

#T_4(2+delta)approxT_4(2)+T'_4(2)delta#

with

#T'_4(x) = -3+2 xx 7(x-2)-3 xx 6(x-2)^2+4 xx 8(x-2)^3#

so

#T'_4(2) = -3#

Finally

#T_4(2+0.1) approx 7-3 xx 0.1 = 6.7#