Practice question · Put in order
Order what the successive Taylor terms make the polynomial match, starting from the centre.
- The rate at which the curvature itself changes
- The curvature of the function at the centre
- The value of the function at the centre
- The slope of the function at the centre
Hints
- Each new term brings in one more derivative.
- The constant term uses no derivative at all.
Show the answer
- The value of the function at the centre
- The slope of the function at the centre
- The curvature of the function at the centre
- The rate at which the curvature itself changes
Why
Value, slope, curvature, then the change in curvature, one extra derivative matched per term. Truncating the series therefore means giving up on matching the higher derivatives, which is why the fit decays as you move away from the centre.
Practise Taylor Series and Approximation
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