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TS EAMCET · Maths · Differentiation

If \(f(x)\left\{\begin{array}{cc}\frac{x-1}{2 x^2-7 x+5}, & \text { for } x \neq 1 \\ -\frac{1}{3} & , \text { for } x=1\end{array}\right.\), then \(f^{\prime}(1)\) is equal to :

  1. A \(-\frac{1}{9}\)
  2. B \(-\frac{2}{9}\)
  3. C \(-\frac{1}{3}\)
  4. D \(\frac{1}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-\frac{2}{9}\)

Step-by-step Solution

Detailed explanation

We have, \(f(x)=\frac{x-1}{2 x^2-7 x+5}, x \neq 1\) \(=\frac{(x-1)}{2 x^2-2 x-5 x+5}\) \(=\frac{x-1}{2 x(x-1)-5(x-1)}=\frac{1}{2 x-5}\) \(f(x)=\left\{\begin{array}{cc}\frac{1}{2 x-5}, & x \neq 1 \\ -\frac{1}{3}, & x=1\end{array}\right.\) Now,…