Question: Find the quadratic polynomial g(x) = ax 2 + bx + c which best fits the function f(x) = e x at x = 0,

Find the quadratic polynomial g(x) = ax2 + bx + c which best fits the function f(x) = ex at x = 0, in the sense that

g(0) = f(0), and g'(0) = f'(0), and g''(0) = f''(0).

Using a computer or calculator, sketch graphs of f and g on the same axes. What do you notice?

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So using g0 f0 etc we have 2a 1 b 1 and c 1 and thus ... View full answer

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