Fourth degree taylor polynomial

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Reference no: EM13118177

The fourth degree Taylor Polynomial for f(x) about x = 3 is:

P4(x) = -1 - (x-1)^2 + 2(x-1)^3 - 4(x-1)^4.

i) Find f^(n)(1) for n = 1, 2, 3, 4.

ii) Show that the function has a local maximum at x = 1.

iii) The fifth derivative of f(x) satisfies |f^(s)(x)| less than or equal to 25000 for all x in [0.8, 1.1].

Use the Lagrange Error Formula to show that Rs(x) is less than or equal to 1/480.

iv) Use part (iii) and P4(x) to find an upper and a lower bound on f(1).

(Hint : Use the fact that f(x) = Pn(x) + Rn(x)).

Reference no: EM13118177

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