Question:
Find a point on the curve $y=3 x^{2}+4$ at which the tangent is perpendicular to the line whose slope is $-\frac{1}{6}$.
Solution:
Given:
The curve $y=3 x^{2}+4$ and the Slope of the tangent is $\frac{-1}{6}$
$y=3 x^{2}+4$
Differentiating the above w.r.t $x$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=2 \times 3 \mathrm{x}^{2-1}+0$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=6 \times \ldots(1)$
Since, tangent is perpendicular to the line,
$\therefore$ The Slope of the normal $=\frac{-1}{\text { The Slope of the tangent }}$
i.e, $\frac{-1}{6}=\frac{-1}{6 x}$
$\Rightarrow \frac{1}{6}=\frac{1}{6 x}$
$\Rightarrow x=1$
Substituting $x=1$ in $y=3 x^{2}+4$
$\Rightarrow y=3(1)^{2}+4$
$\Rightarrow y=3+4$
$\Rightarrow y=7$
Thus, the required point is $(1,7)$.
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- 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
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- Atoms
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