Project ForgeEngineering Mathematics
Numerical Methods
GATE 2014
Medium
If f(x) is a real and continuous function of x, the Taylor series expansion of f(x) about its minima will NEVER have a term containing
- first derivative
- Bsecond derivative
- Cthird derivative
- Dany higher derivative
Explanation
At a minimum x0, f'(x0)=0 by definition (stationary point). The Taylor series f(x)=f(x0)+f'(x0)(x−x0)+f''(x0)(x−x0)²/2!+... therefore has its first-derivative term vanish identically, while second and higher derivative terms generally remain.
Source: GATE CH 2014 (2014)
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