COMEDK · Maths · 27. Application of Derivatives
If the curve \(y=2 x^{3}+a x^{2}+b x+c\) passes through the origin and the tangents drawn to it at \(x=-1\) and \(x=2\) are parallel to the \(X\)-axis, then the values of \(a, b\) and \(c\) are respectively,
- A \(3,-12\) and 0
- B \(-3,12\) and 0
- C \(-3,-12\) and 0
- D \(12,-3\) and 0
Answer & Solution
Correct Answer
(C) \(-3,-12\) and 0
Step-by-step Solution
Detailed explanation
\(y=2 x^{3}+a x^{2}+b x+c...(i)\) Since, it passes through \((0,0)\), \(0=2(0)+a(0)+b(0)+c\) \(\begin{aligned} c &=0 ...(ii)\\ \frac{d y}{d x} &=6 x^{2}+2 a x+b \end{aligned}\) Since, tangents at \(x=-1\) and \(x=2\) are parallel to \(X\)-axis.…
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 line joining two points \(A(2,0) B(3,1)\) is rotated about \(A\) in anticlockwise direction through an angle of \(15^{\circ}\). If \(B\) goes to \(C\) in the new position, then the coordinates of \(C\) isCOMEDK 2024 Medium
- The co-axial system of circles given by \(x^{2}+y^{2}+2 g x+c=0\) for \(c < 0\) representsCOMEDK 2013 Hard
- If \(n(A)=2\) and \(n(B)=3\) then number of relation from set \(A\) to the set \(B\) isCOMEDK 2024 Easy
- Vishnu has two jars of marbles, Jar A and Jar B.
Jar A contains 3 yellow marbles and 2 green marbles.
Jar B contains 4 yellow marbles and 3 green marbles.
Vishnu flips a fair coin.
If it lands heads, he picks two marbles at random without replacement from Jar A.
If it lands tails, he picks two marbles at random with replacement from Jar B.
Given that Vishnu picked one yellow and one green marble, what is the probability that they came from Jar B?COMEDK 2026 Medium - The side of an equilateral triangle expands at the rate of \(\sqrt{3} \mathrm{~cm} / \mathrm{sec}\). When the side is \(12 \mathrm{~cm}\), the rate of increase of its area isCOMEDK 2024 Medium
- If \((p \wedge \sim r) \rightarrow(\sim p \vee q)\) is false, then the truth values of \(p, q\) and \(r\) are respectivelyCOMEDK 2016 Easy
More PYQs from COMEDK
- An element belonging to chalcogen group isCOMEDK 2015 Easy
- The area bounded by the parabola \(y^2=36 x\) and its latus rectum isCOMEDK 2025 Medium
- A vertical circular coil of radius \(0.1 \mathrm{~m}\) and having \(10\) turns carries a steady current. When the plane of the coil is normal to the magnetic meridian, a neutral point is observed at the centre of the coil. If \(B_{H}=0.314 \times 10^{-4} \mathrm{~T}\), the current in the coil isCOMEDK 2013 Medium
- Increasing order of bond order of oxygen and its ions isCOMEDK 2022 Medium
- \(\lim _{x \rightarrow-\infty} \frac{2 x-1}{\sqrt{x^{2}+2 x+1}}\) is equal toCOMEDK 2014 Easy
- \(p\)-toluene sulphonic acid on fusion with solid
KOH at 573 K followed by treatment with dilute
HCl givesCOMEDK 2024 Hard