AP EAMCET · Maths · Application of Derivatives
If \(x\) is real and \(\alpha, \beta\) are maximum and minimum values of \(\frac{x^2-x+1}{x^2+x+1}\) respectively then \(\alpha+\beta=\)
- A \(\frac{10}{3}\)
- B \(\frac{8}{3}\)
- C \(\frac{4}{3}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{10}{3}\)
Step-by-step Solution
Detailed explanation
\(y=\frac{x^2-x+1}{x^2+x+1}\) \(\begin{aligned} & \Rightarrow \frac{d y}{d x}=\frac{(2 x-1)\left(x^2+x+1\right)-(2 x+1)\left(x^2-x+1\right)}{\left(x^2+x+1\right)^2}=0 \\ & \Rightarrow \frac{2 x^2-2}{\left(x^2+x+1\right)^2}=0 \Rightarrow x= \pm 1 \end{aligned}\)…
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 \(\mathrm{P}(\alpha, \beta)\) is a point on the curve \(9 \mathrm{x}^2+4 \mathrm{y}^2=144\) in the first quadrant and the minimum area of the triangle formed by the tangent of the curve at \(P\) with the coordinate axis is S, thenAP EAMCET 2025 Hard
- The equation of a straight line, perpendicular to \(3 x-4 y=6\) and forming a triangle of area 6 sq. units with coordinate axes, isAP EAMCET 2014 Easy
- If \(\int \frac{x^2-x+2}{x^2+x+2} d x=x-\log (f(x))+\frac{2}{\sqrt{7}} \operatorname{Tan}^{-1}(g(x))+c\), then \(\mathrm{f}(-1)+\sqrt{7} \mathrm{~g}(-1)=\)AP EAMCET 2025 Medium
- If the sum of all the coefficients of \(\left(\alpha x^2-2 x+1\right)^{2019}\) is equal to the sum of all the coefficients of \((x-\alpha y)^{2019}\), then \(\alpha=\)AP EAMCET 2020 Easy
- Solve the equation, \(3^{x^2-x}=25-4^{x^2-x}\)AP EAMCET 2020 Easy
- The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?AP EAMCET 2022 Easy
More PYQs from AP EAMCET
- Boron halides usually are Lewi's acids in nature. This is due toAP EAMCET 2020 Medium
- A variable plane passes through a fixed point \((1,2,3)\). Then, the foot of the perpendicular from the origin to the plane lies onAP EAMCET 2013 Easy
- Which one of the following frequencies of radiation (in \(\mathrm{Hz}\) ) has a wavelength of \(600 \mathrm{~nm} ?\)AP EAMCET 2011 Easy
- An ideal gas is taken from state- to state- through optional path and as shown in the diagram. Let and represent the heat supplied, work done and change internal energy respectively, then
AP EAMCET 2021 Hard - Let \(\mathrm{A} \subseteq \mathbb{R}, \mathrm{B} \subseteq \mathbb{R}\) and \(\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}\) be defined by \(\mathrm{f}(\mathrm{x})=\mathrm{x}^2\) \(-3 \mathrm{x}+2\). If \(\mathrm{f}\) is a bijection, thenAP EAMCET 2023 Medium
- The displacement S of a particle measured from a fixed point O on a line is given by \(\mathrm{S}=\mathrm{t}^3-16 \mathrm{t}^2+64 \mathrm{t}-16\). Then the time at which displacement of the particle is maximum isAP EAMCET 2025 Medium