Given the function: f(x) = -18x³ + 45, find the equation of the tangent line, or linear approximation, to the graph of the function at x = 1. L(x) = Use the tangent line to approximate f(1.1). L(1.1) = Compute the actual value of f(1.1). What is the error between the function value and the linear approximation? Answer as a positive value only, and round to 5 decimal places. error] ~
Given the function: f(x) = -18x³ + 45, find the equation of the tangent line, or linear approximation, to the graph of the function at x = 1. L(x) = Use the tangent line to approximate f(1.1). L(1.1) = Compute the actual value of f(1.1). What is the error between the function value and the linear approximation? Answer as a positive value only, and round to 5 decimal places. error] ~
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Given the function: \( f(x) = \sqrt[3]{-18x^3} + 45 \), find the equation of the tangent line, or linear approximation, to the graph of the function at \( x = 1 \).
\[ L(x) = \]
Use the tangent line to approximate \( f(1.1) \).
\[ L(1.1) = \]
Compute the actual value of \( f(1.1) \). What is the error between the function value and the linear approximation?
Answer as a positive value only, and round to 5 decimal places.
\[ | \text{error} | \approx \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03532cdf-3ae3-42ec-b6da-b6f111ab5ca1%2F5eb84b3e-9271-4760-8a62-d6417859b6a5%2Fhusptdj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the function: \( f(x) = \sqrt[3]{-18x^3} + 45 \), find the equation of the tangent line, or linear approximation, to the graph of the function at \( x = 1 \).
\[ L(x) = \]
Use the tangent line to approximate \( f(1.1) \).
\[ L(1.1) = \]
Compute the actual value of \( f(1.1) \). What is the error between the function value and the linear approximation?
Answer as a positive value only, and round to 5 decimal places.
\[ | \text{error} | \approx \]
Expert Solution
Step 1
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
