A) 1
B) -1
C) 0
D) 2
Correct Answer: B
Solution :
We have,
\[Rf'\left( 1 \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f\left( 1-h \right)-f\left( 1 \right)}{-h}\] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{-1}{h}\left[ \frac{{{\left( 1-h \right)}^{2}}}{4}-\frac{3\left( 1-h \right)}{2}+\frac{13}{4}-2 \right]\] \[=\underset{h\to 0}{\mathop{\lim }}\,\left( \frac{1+{{h}^{2}}-2h-6+6h+13-8}{-4h} \right)\] \[=\underset{h\to 0}{\mathop{\lim }}\,\left( \frac{{{h}^{2}}+4h}{-4h} \right)=-1\]
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