Question:
$f(x)=(x-1)(x+2)^{2}$
Solution:
Given: $f(x)=(x-1)(x+2)^{2}$
$\Rightarrow f^{\prime}(x)=(x+2)^{2}+2(x+2)(x-1)$
For a local maximum or a local minimum, we must have
$f^{\prime}(x)=0$
$\Rightarrow(x+2)^{2}+2(x+2)(x-1)=0$
$\Rightarrow(x+2)(x+2+2 x-2)=0$
$\Rightarrow(x+2)(3 x)=0$
$\Rightarrow x=0,-2$
Since $f^{\prime}(x)$ changes from negative to positive when $x$ increases through $0, x=0$ is the point of local minima. The local minimum value of $f(x)$ at $x=0$ is given by
$(0-1)(0+2)^{2}=-4$
Since $f^{\prime}(x)$ changes sign from positive to negative when $x$ increases through $-2, x=-2$ is the point of local maxima. The local maximum value of $f(x)$ at $x=-2$ is given by
$(-2-1)(-2+2)^{2}=0$
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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
- Ray Optics and Optical Instruments
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- Dual Nature of Radiation and Matter
- Atoms
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- Chemical Effects of Electric Current,
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