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 :
- A \(-\frac{1}{9}\)
- B \(-\frac{2}{9}\)
- C \(-\frac{1}{3}\)
- D \(\frac{1}{3}\)
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,…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(x\) is numerically so small so that \(x^2\) and higher powers of \(x\) can be neglected, then \(\left(1+\frac{2 x}{3}\right)^{3 / 2} \cdot(32+5 x)^{-1 / 5}\) is approximately equal toTS EAMCET 2009 Easy
- The points in the Argand plane given by form aTS EAMCET 2018 Easy
- If \(A+B+C=2 S\), then \(\sin (S-A)+\sin (S-B)-\sin C=\)TS EAMCET 2018 Medium
- The approximate value of \(\tan ^1\) (0.999) (upto 4 decimal places) isTS EAMCET 2019 Easy
- The solution of \(\left(1+x^2\right) \frac{d y}{d x}+2 x y-4 x^2=0\) is :TS EAMCET 2006 Medium
- \(P\) is a \(3 \times 3\) square matrix and \(\operatorname{Tr}(P) \neq 0\). If \(\operatorname{Tr}\left(\mathrm{P}-\mathrm{P}^{\mathrm{T}}\right)+\operatorname{Tr}\left(\mathrm{P}+\mathrm{P}^{\mathrm{T}}\right)+\frac{\operatorname{Tr}(P)}{\operatorname{Tr}\left(P^T\right)}+\operatorname{Tr}(\mathrm{P}) \times \operatorname{Tr}\left(\mathrm{P}^{\mathrm{T}}\right)=\) 0 then \(\operatorname{Tr}(\mathrm{P})=\)TS EAMCET 2023 Medium
More PYQs from TS EAMCET
- A block of mass \(10 \mathrm{~kg}\), initially at rest, makes a downward motion on \(45^{\circ}\) inclined plane. Then the distance travelled by the block after \(2 \mathrm{~s}\) is (Assume the coefficient of kinetic friction to be 0.3 and \(g=10 \mathrm{~ms}^{-2}\) )TS EAMCET 2019 Hard
- Identify the incorrect statement from the following?TS EAMCET 2025 Medium
- The correct order of enthalpy of vaporisation of noble gases isTS EAMCET 2022 Easy
- Which of the options correctly represent the basicity for these compounds?
TS EAMCET 2018 Easy - The reaction \(2 \mathrm{~A} \rightarrow 2 \mathrm{~B}+\mathrm{C}\) has a rate constant of \(1.2 \times 10^{-2} \mathrm{~s}^{-1}\). Which of the following is correct?TS EAMCET 2022 Medium
- Let be the set of all real numbers. Let be a function defined by Match the following
The correct match isList-I List-II (A) (I) (B) (II) (C) (III) (D) (IV) (V) TS EAMCET 2022 Easy