CUET · MATHS · PYQ PAPER 2023
If the function \(f(x)=x^2+k x+7\) is strictly increasing in the interval [-2, 2], then
- A \(K<4\)
- B \(K>4\)
- C \(K<-4\)
- D \(K>-4\)
Answer & Solution
Correct Answer
(B) \(K>4\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^2+k x+7\) \(f'(x)=2x+k\) For \(f(x)\) to be strictly increasing in \([-2, 2]\), \(f'(x) > 0\) for all \(x \in [-2, 2]\). The minimum value of \(f'(x)\) in \([-2, 2]\) occurs at \(x=-2\). \(f'(-2) > 0\) \(2(-2)+k > 0\) \(-4+k > 0\) \(k > 4\)
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
- \(\int e^x\left(\frac{1-x}{1+x^2}\right)^2\) \(dx\) is equal toCUET 2025 Hard
- The diagonal elements of a skew symmetric matrix are allCUET 2025 Medium
- The mean of the number of heads in a simultaneous toss of three coins isCUET 2025 Medium
- For \(x>1, \int \frac{e^{7 \log x}-e^{5 \log x}}{e^{5 \log x}-e^{4 \log x}} d x\) equals.CUET 2025 Easy
- The area bounded by the curve \(y=x^2\) between \(x=0\) and \(x=\pi\), in the first quadrant is :CUET 2023 Easy
- The integrating factor of the differential equation \(x \frac{d y}{d x}-y=\sin x\) is :CUET 2023 Medium
More PYQs from CUET
- When a ray of light enters a glass slab from air :CUET 2023 Hard
- Typical embryo sac at maturity is:CUET 2025 Easy
- The maximum value of the determinant of the matrix \(\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+\sin x & 1 \\ 1+\cos x & 1 & 1\end{array}\right]\)
(where \(x\) is real) is :CUET 2025 Hard - The value of \(\lambda\) and \(\mu\) if \((2 \hat{i}+6 \hat{j}+27 \hat{k}) \times(\hat{i}+\lambda \hat{j}+\mu \hat{k})=\overrightarrow{0}\) are respectively :CUET 2023 Medium
- Choose the correct statements about interstitial compounds from the following:
(A) They have low melting points, lower than those of pure metals
(B) They are perfect-stoichiometric compounds
(C) These are formed when small atoms like H, C or N are trapped inside the crystal lattices of metals
(D) They are neither typically ionic nor covalent
Choose the correct answer from the options given below:CUET 2025 Easy - \(f(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\\frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\)
is continuous in the interval \([-1,1]\), then \(p\) is equal to :CUET 2023 Hard