Question:
Let $S$ be the set of all values of $x$ for which the tangent to the curve $\mathrm{y}=f(\mathrm{x})=\mathrm{x}^{3}-\mathrm{x}^{2}-2 \mathrm{x}$ at $(x, y)$ is parallel to the line segment joining the points $(1, f(1))$ and $(-1, f(-1))$, then $\mathrm{S}$ is equal to :
$\left\{-\frac{1}{3},-1\right\}$
$\left\{\frac{1}{3},-1\right\}$
$\left\{-\frac{1}{3}, 1\right\}$
$\left\{\frac{1}{3}, 1\right\}$
Correct Option: , 3
Solution:
$f(1)=1-1-2=-2$
$f(-1)=-1-1+2=0$
$\mathrm{m}=\frac{f(1)-f(-1)}{1+1}=\frac{-2-0}{2}=-1$
$\frac{d y}{d x}=3 x^{2}-2 x-2$
$3 x^{2}-2 x-2=-1$
$\Rightarrow 3 x^{2}-2 x-1=0$
$\Rightarrow(x-1)(3 x+1)=0$
$\Rightarrow x=1,-\frac{1}{3}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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