A) \[f(x)=f(-x),\] for all x
B) \[f(x)\ne 1,\] for \[x=0\]
C) \[f''(x)>0,\] for all x
D) \[f(x)>1,\] for \[x\le 1\]
Correct Answer: C
Solution :
Given that, \[f(x)={{x}^{2}}+4x+1\] \[f'(x)=2x+4\] For maxima or minima, put \[f'(x)=0\] \[\Rightarrow \] \[2x+4=0\] \[\Rightarrow \] \[x=-2\] Now, \[f''(x)=2>0\]
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