# calculus

posted by Meredith

The function f has derivatives of all orders for all real numbers x. Assume f(2)=-3, f'(2)=5, f''(2)=3, and f'''(2)=-8.
The fourth derivative of f satisfies the inequality, the (absolute value of f''''(x)) <=3 for all x in the closed interval [1.5, 2]. Use the Lagrange error bound on the approximation to f(1.5) found in part (a) to explain why f(1.5) does not equal -5.

The part (a) was where I wrote the third-degree Taylor polynomial for f about x=2 and approximate f(1.5).
I had -3+5(x-2) +3(x-2)^2/2-8(x-2)^3/6, which was -4.958333 when f(1.5).

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