Show that the tangents to the curve $y=7 x^{3}+11$ at the points $x=2$ and $x=-2$ are parallel.
Given:
The curve $y=7 x^{3}+11$
Differentiating the above w.r.t $\mathrm{x}$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=3 \times 7 \times^{3-1}+0$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=21 \times^{2}$
when $x=2$'
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}_{\mathrm{x}}=2}=21 \times(2)^{2}$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}_{\mathrm{x}}=2}=21 \times 4$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{d} \mathrm{x}_{\mathrm{x}}=2}=84$
when $x=-2$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}_{\mathrm{x}}=2}=21 \times(-2)^{2}$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}_{\mathrm{x}}=2}=21 \times 4$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}_{\mathrm{x}}=2}=84$
Let $y=f(x)$ be a continuous function and $P\left(x_{0}, y_{0}\right)$ be point on the curve, then,
The Slope of the tangent at $P(x, y)$ is $f^{\prime}(x)$ or $\frac{d y}{d x}$
Since, the Slope of the tangent is at $x=2$ and $x=-2$ are equal, the tangents at $x=2$ and $x=-2$ are parallel.
- 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,
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,