Question

The derivative of f(x) = $\left\{ \begin{matrix} \frac{x–1}{2x^{2}–7x + 5}, & x \neq 1 \\ –\frac{1}{3}, & x = 1 \end{matrix} \right.\$ at x = 1 is –

• A. $–\frac{2}{9}$
• B. – $\frac{2}{44}$
• C. 0
• D. None of these

Answer 1

Answer: (A)

$–\frac{2}{9}$

Answer 2

f(x) = $\left\{ \begin{matrix} \frac{1}{2x–5}, & x \neq 1 \\ –\frac{1}{3}, & x = 1 \end{matrix} \right.\$

f ′(x) = $\frac{–2}{(2x–5)^{2}}$ ⇒ f ′(1) = – $\frac{2}{9}$.