Functions Question 319
Question: If $ f(x),= \begin{cases} \frac{x-1}{2x^{2}-7x+5} & \text{for }x\ne 1 \\ -\frac{1}{3} & \text{for }x=1 \\ \end{cases}, . $ then $ f’(1)= $
[EAMCET 2003]
Options:
A) ?1/9
B) ?2/9
C) ?1/3
D) 1/3
Show Answer
Answer:
Correct Answer: B
Solution:
By definition, $ {f}’(1)=\underset{h\to 0}{\mathop{\lim }},\frac{f(1+h)-f(1)}{h} $ $ =\underset{h\to 0}{\mathop{\lim }},\frac{\frac{1}{2(1+h)-5}-( \frac{-1}{3} )}{h}=\underset{h\to 0}{\mathop{\lim }},\frac{( \frac{1}{2h-3}+\frac{1}{3} )}{h} $ $ =\underset{h\to 0}{\mathop{\lim }},( \frac{3+2h-3}{3h(2h-3)} )=\underset{h\to 0}{\mathop{\lim }},( \frac{2h}{3h(2h-3)} ) $ $ =\underset{h\to 0}{\mathop{\lim }},\frac{2}{3(2h-3)}=\frac{2}{3(-3)}=\frac{-2}{9} $ .
BETA
