Q. If $f(x) = \left\{ \begin{array}{r} \frac{x - 1}{2x^{2} - 7x + 5},\ \ \ for\ x \neq 1 \\ - \frac{1}{3},\ \ for\ \ x = 1 \end{array} \right.\$, then $f^{'}(1)$ is equal to
A) $- \frac{1}{9}$
B) $- \frac{2}{9}$
C) $- 13$
D) 1/3
Explanation
(b)
$f^{'}(1) = \lim_{h \rightarrow 0}\ \frac{f(1 + h) - f(1)}{h}$
$= \lim_{h \rightarrow 0}\ \frac{\frac{1 + h - 1}{2(1 + h)^{2} - 7(1 + h) + 5}—\left( \frac{1}{3} \right)\ }{h}$
$= \lim_{h \rightarrow 0}\frac{\left( \frac{1}{2h - 3} + \frac{1}{3} \right)}{h} = \lim_{h \rightarrow 0}\left( \frac{2h}{3h(2h - 3)} \right) = - \frac{2}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.