Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
a) f(x)=5x²e²x

a) f(x)=5x²e²x

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
Question
100%
Find the derivative of this function but Do Not Simplify
a) \( f(x) = 5x^3 e^{2x} \) This function, \( f(x) \), is a product of two components: a polynomial, \( 5x^3 \), and an exponential function, \( e^{2x} \). - **Polynomial Component:** The term \( 5x^3 \) is a cubic polynomial. The coefficient 5 indicates the steepness of the curve, and \( x^3 \) suggests that the function will have one inflection point and exhibit growth at an increasing rate as \( x \) becomes larger. - **Exponential Component:** The term \( e^{2x} \) represents an exponential growth function, where \( e \) is the base of the natural logarithm, approximately equal to 2.71828. The exponent \( 2x \) shows that the exponential growth rate is twice the rate of a standard exponential function, \( e^x \). Together, this function \( f(x) \) describes a curve that grows rapidly, influenced by both the polynomial and exponential components. The exponential factor will generally dominate as \( x \) increases, causing rapid growth in the value of \( f(x) \).
Transcribed Image Text:a) \( f(x) = 5x^3 e^{2x} \) This function, \( f(x) \), is a product of two components: a polynomial, \( 5x^3 \), and an exponential function, \( e^{2x} \). - **Polynomial Component:** The term \( 5x^3 \) is a cubic polynomial. The coefficient 5 indicates the steepness of the curve, and \( x^3 \) suggests that the function will have one inflection point and exhibit growth at an increasing rate as \( x \) becomes larger. - **Exponential Component:** The term \( e^{2x} \) represents an exponential growth function, where \( e \) is the base of the natural logarithm, approximately equal to 2.71828. The exponent \( 2x \) shows that the exponential growth rate is twice the rate of a standard exponential function, \( e^x \). Together, this function \( f(x) \) describes a curve that grows rapidly, influenced by both the polynomial and exponential components. The exponential factor will generally dominate as \( x \) increases, causing rapid growth in the value of \( f(x) \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS