Question:
The minimum value of $\mathrm{f}(\mathrm{x})=x 4-x 2-2 x+6$ is
(a) 6
(b) 4
(c) 8
(d) none of these
Solution:
(b) 4
Given : $f(x)=x^{4}-x^{2}-2 x+6$
$\Rightarrow f^{\prime}(x)=4 x^{3}-2 x-2$
$\Rightarrow f^{\prime}(x)=(x-1)\left(4 x^{2}+4 x+2\right)$
For a local maxima or a local minima, we must have
$f^{\prime}(x)=0$
$\Rightarrow(x-1)\left(4 x^{2}+4 x+2\right)=0$
$\Rightarrow(x-1)=0$
$\Rightarrow x=1$
Now,
$f^{\prime \prime}(x)=12 x^{2}-2$
$\Rightarrow f^{\prime \prime}(1)=12-2=10>0$
So, $x=1$ is a local minima.
The local minimum value is given by
$f(1)=1-1-2+6=4$
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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
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- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
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- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
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- 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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