CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=x^3-3 x\) is :
- A Increasing in \((0, \infty)\) and decreasing in \((-\infty, 0)\)
- B Decreasing in \((0, \infty)\) and increasing in \((-\infty, 0)\)
- C Decreasing in \((-\infty,-1] \cup[1, \infty)\) and increasing in \((-1,1)\)
- D Increasing in \((-\infty,-1] \cup[1, \infty)\) and decreasing in \((-1,1)\)
Answer & Solution
Correct Answer
(D) Increasing in \((-\infty,-1] \cup[1, \infty)\) and decreasing in \((-1,1)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 3x^2 - 3\) \(3x^2 - 3 = 0 \implies x^2 = 1 \implies x = \pm 1\) \(f'(x) > 0\) for \(x \in (-\infty, -1) \cup (1, \infty)\) \(f'(x) Increasing in \((-\infty,-1] \cup[1, \infty)\) and decreasing in \((-1,1)\)
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
- A car starts from a point \(P\) at time \(t=0\) seconds and stops at \(Q\).
The distance \(x\), in meters, covered by it in \(t\) seconds is given by \(x(t)=t^3\left(3-\frac{t^2}{5}\right)\).
The distance between \(P\) and \(Q\) is:CUET 2023 Easy - If \(A\) is a square matrix such that \(A^2=A\) and \(I\) is the identify matrix of the same order as \(A\) then \((I+2 A)^3-6 A\) is equal toCUET 2025 Easy
- If an asset costs Rs. 50,000 with an estimated useful life of 6 years and a scrap value of Rs. 5000. Then by using a linear depreciation method, the annual depreciation of the asset will be:CUET 2025 Easy
- The amount to which ₹ 5000 will accumulate at the effective rate of 4% for 4 years and 5% for 2 years is:CUET 2025 Easy
- \(\int e^{(x \log 5)} e^x d x\), is :
Where \(c\) is the constant of integration.CUET 2025 Hard - If A is a square matrix such that \(A^2=A\) and I is the identity matrix of same order as A, then the value of
\((A-2 I)^2-(2 A+I)^2+11 A\) is :CUET 2025 Easy
More PYQs from CUET
- The value of the integral \(I=\int_0^1 \frac{1}{\sqrt{1+3 \sqrt{x}}} d x\) is:CUET 2025 Hard
- An electron enters a crossed electrical and magnetic field region with a speed of \( 100 \text{ m s}^{-1} \) along \( +x \)-axis and passes undeviated. The strength of magnetic field is 5.0 T and it acts along \( +z \)-axis. Give the electrical field in vector notations indicating its magnitude as well as direction :CUET 2023 Easy
- Given that two identical coils, one of copper and another of aluminium are rotated with the same angular speed in an external magnetic field, which of the following statements is true?CUET 2025 Medium
- Let \(A, B, C\) be matrices of order \(p \times k, 3 \times k\) and \(n \times 3\) respectively, then the conditions on \(n, k\) and \(p\) so that \(A B+C B\) will be defined are :CUET 2023 Medium
- Select the correct statements for [Fe(CN)6]3- complex :
(A) Paramagnetic
(B) sp3d2 hybridization
(C) Magnetic moment = 5.92 BM
(D) d2sp3 hybridization
Choose the correct answer from the options given below :CUET 2025 Medium - A surface of area \( \vec{A} = 2\hat{i} - 3\hat{k} \) exists in a region of electric field \( \vec{E} = a\hat{i} + b\hat{j} \). The net flux passing through the surface isCUET 2025 Easy