COMEDK · Maths · 27. Application of Derivatives
If a tangent to the curve \(y=6 x-x^{2}\) is parallel to the line \(4 x-2 y-1=0\), then the point of tangency on the curve is
- A \((2,8)\)
- B \((8,2)\)
- C \((6,1)\)
- D \((4,2)\)
Answer & Solution
Correct Answer
(A) \((2,8)\)
Step-by-step Solution
Detailed explanation
Let \(P\left(x_{1}, y_{1}\right)\) be the required point. The given curve is \[ \begin{aligned} y &=6 x-x^{2} \\ \Rightarrow \quad \frac{d i j}{d x} &=6-2 x \\ \Rightarrow \quad\left(\frac{d y}{d x}\right)_{\left(x_{1}, \mathfrak{h}\right)} &=6-2 x_{1} \end{aligned} \] Since,…
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
- If \(\log y = \log(\sin x) - x^2\), then \(\dfrac{d^2y}{dx^2} + 4x\dfrac{dy}{dx} + 4x^2y =\)COMEDK 2026 Medium
- If the straight lines \(\dfrac{x-2}{1}=\dfrac{y-3}{1}=\dfrac{z-4}{-t}\) and \(\dfrac{x-1}{t}=\dfrac{y-4}{2}=\dfrac{z-5}{1}\) are intersecting then \(t\) can haveCOMEDK 2024 Medium
- If \(A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 4\end{array}\right], B=\left[\begin{array}{c}7 \\ 16 \\ 22\end{array}\right], X=\left[\begin{array}{c}x \\ y \\ z\end{array}\right]\) and \(A X=B\), then \(z\) is equal toCOMEDK 2012 Easy
- \(\int \tan^{-1}\left(\sqrt{\dfrac{1 - \sin x}{1 + \sin x}}\right)\, dx =\)COMEDK 2026 Medium
- The ends of the latusrectum of the parabola \(x^{2}+10 x-16 y+25=0\) areCOMEDK 2018 Easy
- The tangent and the normal drawn to the curve \(y=x^{2}-x+4\) at \(P(1,4)\) cut the \(X\)-axis at \(A\) and \(B\) respectively. If the length of the subtangent drawn to the curve at \(P\) is equal to the length of the subnormal, then the area of the \(\triangle P A B\) in square units is,COMEDK 2016 Medium
More PYQs from COMEDK
- A first order reaction proceeds to \(90 \%\) completion. What will be the approximate time taken for \(90 \%\) completion in relation to \(t_{1 / 2}\) of the reaction?COMEDK 2023 Medium
- When a current of 2.5 A passes through the primary coil of a transformer of 200 number turns, the magnetic flux linked with the secondary coil having 400 turns is \(600 \times 10^{-6}\ T\ m^2\). Find the induced emf in the secondary coil, when the current in the primary coil increases at a rate of \(0.2\ As^{-1}\)COMEDK 2026 Medium
- When the combustion of one molecule of liquid heptane is carried out at a constant temperature ' \(T\) ', the difference between \(\Delta H^o\) and \(\Delta U^o\) is equal to:COMEDK 2025 Medium
- Minimum mumber of nodes are present inCOMEDK 2022 Medium
- The radius of the circle passing through the point \((6,2)\) and two of whose diameters are \(x+y=6\) and \(x+2 y=4\) isCOMEDK 2013 Easy
- The feasible region represented by the constraints:
\(x + 2y \leq 120\);
\(x + y \geq 60\);
\(x - 2y \geq 0\);
\(x \geq 0\) and \(y \geq 0\)COMEDK 2026 Easy