Question:
Find the intervals in which $f(x)=(x+2) e^{-x}$ is increasing or decreasing ?
Solution:
we have,
$f(x)=(x+2) e^{-x}$
$f^{\prime}(x)=e^{-x}-e^{-x}(x+2)$
$=e^{-x}(1-x-2)$
$=-e^{-x}(x+1)$
Critical points
$f^{\prime}(x)=0$
$\Rightarrow-e^{-x}(x+1)=0$
$\Rightarrow x=-1$
Clearly $\mathrm{f}^{\prime}(\mathrm{x})>0$ if $\mathrm{x}<-1$
$\mathrm{f}^{\prime}(\mathrm{x})<0$ if $\mathrm{x}>-1$
Hence $f(x)$ increases in $(-\infty,-1)$, decreases in $(-1, \infty)$
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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
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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