Suppose f(0) = 4, f'(0) = 2, f''(0) = 2, and f(3) (0) = 6. Find the third-order Taylor polynomial for f centered at 0 and use it to approximate f(0.1). The third-order polynomial is p3(x) = 4+2x+x²+x² (Simplify your answer.) The value of f(0.1) is approximately p3 (0.1) = (Simplify your answer.)

Suppose f(0) = 4, f'(0) = 2, f''(0) = 2, and f(3) (0) = 6. Find the third-order Taylor polynomial for f centered at 0 and use it to approximate f(0.1). The third-order polynomial is p3(x) = 4+2x+x²+x² (Simplify your answer.) The value of f(0.1) is approximately p3 (0.1) = (Simplify your answer.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 3E

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Suppose f(0) = 4, f'(0) = 2, f''(0) = 2, and f(3) (0) = 6. Find the third-order Taylor polynomial for f centered at 0 and use it to approximate f(0.1).
The third-order polynomial is p3(x) = 4 + 2x + x² + x² (Simplify your answer.)
The value of f(0.1) is approximately P3 (0.1) = (Simplify your answer.)
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