Consider f, a function such as f(2) = 1, f'(2) = 2, f''(2) = 3 and f'''(2) = 4 and that verifies: -3 < f(x) < 34 0 < f'(x) < 12 -8 < f''(x) < 9 -6 < f'''(x) < 5 for all x ∈ [0,4]. Find the second degree Taylor polynomial, T2(x), of f at a = 2, then use T2(x) to approximate f(1) and determine a bound on the approximation error. Give a bound on the approximation error f(x) ≈ T2(x) that is valid for all x in the interval [0,4].

Consider f, a function such as f(2) = 1, f'(2) = 2, f''(2) = 3 and f'''(2) = 4 and that verifies: -3 < f(x) < 34 0 < f'(x) < 12 -8 < f''(x) < 9 -6 < f'''(x) < 5 for all x ∈ [0,4]. Find the second degree Taylor polynomial, T2(x), of f at a = 2, then use T2(x) to approximate f(1) and determine a bound on the approximation error. Give a bound on the approximation error f(x) ≈ T2(x) that is valid for all x in the interval [0,4].

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.4: Definition Of The Derivative

Problem 6YT

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