COMEDK · Maths · 28. Indefinite Integration
The least value of the function \(f(x)=a x+\dfrac{b}{x}, \quad(x>0, b>0, a>0)\) is
- A \(2 \sqrt{a b}\)
- B \(a b\)
- C \(\sqrt{a b}\)
- D \(2 a b\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{a b}\)
Step-by-step Solution
Detailed explanation
The function is given by \(f(x) = ax + \dfrac{b}{x}\) for \(x > 0\), \(a > 0\), and \(b > 0\). Since \(ax > 0\) and \(\dfrac{b}{x} > 0\), we can apply the Arithmetic Mean-Geometric Mean (AM-GM) inequality, which states that for positive real numbers \(u\) and \(v\),…
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
- The function \(f(x)=\left(\frac{\log _{e}(1+a x)-\log _{e}(1-b x)}{x}\right)\) is
undefined at \(x=0\). The value which should be assigned to \(f\) at \(x=0\) so that it is continuous at \(x=0\) isCOMEDK 2018 Medium - The general solution of the differential equation \(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\)COMEDK 2023 Medium
- The remainder when \(7^{103}\) is divided by \(25\) isCOMEDK 2026 Medium
- The number of common tangent to the circle \(x^2+y^2=9\) and \(x^2+y^2-6 x-8 y+21=0\)COMEDK 2024 Medium
- The line \(\dfrac{x-3}{4}=\dfrac{y-4}{5}=\dfrac{z-5}{6}\) is parallel to the planeCOMEDK 2022 Medium
- A random variable X with probability distribution is given below
\(X = x_i\) 2 3 4 5 \(P(X = x_i)\) \(\dfrac{5}{k}\) \(\dfrac{7}{k}\) \(\dfrac{9}{k}\) \(\dfrac{11}{k}\) COMEDK 2024 Medium
More PYQs from COMEDK
- The value of \((0.2) \log _{\sqrt{5}}\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \infty\right)\) isCOMEDK 2018 Easy
- \(\int \dfrac{x}{(x-1)(x-2)^2} d x=a \log \left|\dfrac{x-1}{x-2}\right|+\dfrac{b}{(x-2)}+c\) thenCOMEDK 2025 Medium
- If \(A=\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right|\) and \(B=\left|\begin{array}{ccc}c_{1} & c_{2} & c_{3} \\ a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3}\end{array}\right|\) thenCOMEDK 2019 Medium
- \(5\text{ g}\) of a non-volatile, water-soluble compound \(X\) is dissolved in \(100\text{ g}\) of water (\(K_b = 0.52\text{ K kg mol}^{-1}\)). The elevation in boiling point is found to be \(1.3\text{ K}\). The molar mass of compound \(X\) is:COMEDK 2023 Medium
- The maximum kinetic energy of emitted electrons in a photoelectric effect does not depend uponCOMEDK 2018 Easy
- Three houses are available in a locality. Three persons apply for the houses.
Each applies for one house without consulting others. The probability that all three apply for the same house isCOMEDK 2025 Easy