A) \[-2.125\]
B) \[2.125\]
C) \[-2.812\]
D) \[2.812\]
Correct Answer: A
Solution :
We have,\[{{x}_{2}}={{x}_{0}}-\frac{{{x}_{1}}-{{x}_{0}}}{f({{x}_{1}})-f({{x}_{0}})}\] Here,\[{{x}_{0}}=-3,\,\,{{x}_{1}}=-2,\,\,f(x)={{x}^{3}}-3x+4\] \[\therefore \] \[f({{x}_{0}})=-27+9+4=-14\] \[f({{x}_{1}})=-8+6+4=2\] So, \[{{x}_{2}}=-3-\frac{1}{16}\times (-14)\] \[=-3+\frac{7}{8}=-\frac{17}{8}=-2.125\]
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