Question:
Let $f(x)=2 x^{3}-3 x^{2}-12 x+5$ on $[-2,4]$. The relative maximum occurs at $x=$
(a) $-2$
(b) $-1$
(C) 2
(d) 4
Solution:
(c) 2
Given : $f(x)=2 x^{3}-3 x^{2}-12 x+5$
$\Rightarrow f^{\prime}(x)=6 x^{2}-6 x-12$
For a local maxima or a local minima, we must have
$f^{\prime}(x)=0$
$\Rightarrow 6 x^{2}-6 x-12=0$
$\Rightarrow x^{2}-x-2=0$
$\Rightarrow(x-2)(x+1)=0$
$\Rightarrow x=2,-1$
Now,
$f^{\prime \prime}(x)=12 x-6$
$\Rightarrow f^{\prime \prime}(-1)=-12-6=-18<0$
So, $x=1$ is a local maxima.
Also,
$f^{\prime \prime}(2)=24-6=18>0$
So, $x=2$ is a local minima.
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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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