CUET · MATHS · PYQ PAPER 2023
The second order derivative of \(x^3\) log x is:
- A \(x(5+6 \log x)\)
- B \(x(2+3 \log x)\)
- C \(5 x+6 \log x\)
- D \(3 x+6 \log x\)
Answer & Solution
Correct Answer
(A) \(x(5+6 \log x)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{d}{dx}(x^3 \log x) = 3x^2 \log x + x^3 \cdot \frac{1}{x} = 3x^2 \log x + x^2\) \(f''(x) = \frac{d}{dx}(3x^2 \log x + x^2) = (6x \log x + 3x^2 \cdot \frac{1}{x}) + 2x\) \(f''(x) = 6x \log x + 3x + 2x = 6x \log x + 5x\) \(f''(x) = x(5 + 6 \log x)\)
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
- Consider \(f(x)=\sin (3 x)+4, \forall x \in \mathbb{R}\)
(A) Maximum value of f(x) is 5
(B) Maximum value of f(x) is 3
(C) Maximum value of f(x) is attained at \(x=\frac{\pi}{3}\)
(D) Minimum value of f(x) is attained at x = 0
Choose the correct answer from the options given below:CUET 2025 Medium - If the vectors \(\hat{i}-2 x \hat{j}+3 y \hat{k}\) and \(\hat{i}+2 x \hat{j}-3 y \hat{k}\) are perpendicular, then the locus of \((x, y)\) is:CUET 2023 Hard
- The function \(f(x)=\left|\begin{array}{cc}x^2 & x \\ 3 & 1\end{array}\right|, x \in R\) has a:CUET 2023 Medium
- The slope of the normal to the curve \(y=2 x^2-4\) at \(P(1,-2)\) is:CUET 2023 Medium
- A relation \(f: N \rightarrow N\) be defined by \(f(x)=x^2, x \in N\) (Set of Natural numbers), Then \(f(x)\) isCUET 2025 Medium
- Pipe A can fill a tank in 24 hours and pipe B in 32 hours. If both the pipes are opened in an empty tank at the same time, then the time taken to fill the tank is:CUET 2025 Hard
More PYQs from CUET
- Match List - I with List - II.
List - I (Electronic Device) List - II (Application) (A) Zener diode (I) Rectifier (B) Capacitor (II) Amplifier (C) Transistor (III) Voltage regulator (D) p-n junction diode (IV) Filter circuit
Choose the correct answer from the options given below :CUET 2023 Hard - Consider the following hypothesis test :
\( H_0 : \mu=18 \)
\( H_1 : \mu \neq 18 \)
If a sample of 48 provided a sample mean \(\bar{x}=17\),
and a sample standard deviation \(\sigma=4.5\),
then the value of the \(t\)-test statistic is :CUET 2025 Easy - The function \(f(x)=\tan x-x\) for \(x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\) is :CUET 2023 Easy
- Read the passage below and answer the question:
The accumulation of molecular species at the surface rather than in the bulk of a solid or liquid is termed as adsorption. There are two types of adsorption. In physisorption, attractive forces are mainly Van der Waals while in chemical adsorption adsorbate is held with chemical bonds adsorbent. Adsorption increases with increase in pressure and decreases as temperature is increased.
Which of the following is not application of adsorption?CUET 2023 Medium - Which is an example of homology?CUET 2023 Easy
- The fluid filled cavity present in the secondary follicle is known as:CUET 2025 Easy