Question:
At what points will be tangents to the curve $y=2 x^{3}-15 x^{2}+36 x-21$ be parallel to the $x$ - axis? Also, find the equations of the tangents to the curve at these points.
Solution:
finding the slope of the tangent by differentiating the curve
$\frac{d y}{d x}=6 x^{2}-30 x+36$
According to the question, tangent is parallel to the $x$-axis, which implies $m=0$
$6 x^{2}-30 x+36=0$
$x^{2}-5 x+6=0$
$x=3$ or $x=2$
since this point lies on the curve, we can find $y$ by substituting $x$
$y=2(3)^{3}-15(3)^{2}+36(3)-21$
$y=6$
or
$y=2(2)^{3}-15(2)^{2}+36(2)-21$
$y=7$
equation of tangent is given by $y-y_{1}=m($ tangent $)\left(x-x_{1}\right)$
$y-6=0(x-3)$
$y=6$
or
$y-7=0(x-2)$
$y=7$
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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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