COMEDK · Maths · 27. Application of Derivatives
The range in which \(y=-x^{2}+6 x-3\) is increasing, is
- A \(x>3\)
- B \(x < 3\)
- C \(5 < x < 6\)
- D \(7 < x < 8\)
Answer & Solution
Correct Answer
(B) \(x < 3\)
Step-by-step Solution
Detailed explanation
We have, \[ y=-x^{2}+6 x-3 \Rightarrow \frac{d y}{d x}=-2 x+6 \] Now, for increasing \[ \begin{aligned} & \frac{d y}{d x}>0 \Rightarrow-2 x+6>0 \\ \Rightarrow \quad 2 x & < 6 \quad \Rightarrow x < 3 \end{aligned} \] So, for \(x < 3, f(x)\) is increasing.
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 slope of lines which makes an angle \(45^{\circ}\) with the line \(2 x-y=-7\)COMEDK 2022 Easy
- The total number of terms in the expansion of \((x+y)^{100}+(x-y)^{100}\) isCOMEDK 2022 Easy
- If \(a>b>0\), then the value of \(\tan ^{-1}\left(\frac{a}{b}\right)+\tan ^{-1}\left(\frac{a+b}{a-b}\right)\) depends onCOMEDK 2016 Easy
- If two lines \(L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\) and \(L_2: \frac{x-3}{1}=\frac{y-k}{2}=z\) intersect at a point, then \(2 k\) is equal toCOMEDK 2023 Medium
- If \(\quad X=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\) and \(Y=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]\) and \(B=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\) then \(B\) equalsCOMEDK 2025 Easy
- If \(k\) is the arithmetic mean of two given quantities and \(p, q\) are the geometric means between the same two quantities, then \(p^3 + q^3\) is:COMEDK 2026 Medium
More PYQs from COMEDK
- A tangent galvanometer has a reduction factor of \(1 \mathrm{~A}\) and it is placed with the plane of its coil perpendicular to the magnetic meridian. The deflection produced when a current of \(I A\) is passed through it isCOMEDK 2017 Medium
- If \(f(x)=\frac{2 x-3}{3 x+4}\), then \(f^{-1}\left(\frac{-4}{3}\right)=\)COMEDK 2014 Easy
- The perpendicular distance of a line from the origin is 5 units and its slope is \(-1\).
The equation of the line isCOMEDK 2024 Easy - Which of the following is not true for a perfect conductor?COMEDK 2025 Medium
- Identify the pair of molecules in which one of them is a molecule with an odd electron and the other has an expanded octet.COMEDK 2024 Medium
- Three point charges are located on a circular arc at A, B and C as shown in the figure below. The total electric field at the centre of the arc (0) is
COMEDK 2024 Medium