Question: Consider the 1-variable function f1x2! x3 - 3x2 + 11x at current point x = 3. (a) Derive the first-order Taylor approximation to f1x +

Consider the 1-variable function f1x2! x3 -

3x2 + 11x at current point x = 3.

(a) Derive the first-order Taylor approximation to f1x + l2.

(b) Derive the second-order Taylor approximation to f1x + l2.

(c) Plot the original function and both Taylor series approximations in the vicinity of x.

How accurate do the approximations appear to be? Which is better?

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