Question

Linear approximation Estimate $f(3.85)$ given that $f(4)=3$ and $f^{\prime}(4)=2$.

   Linear approximation Estimate $f(3.85)$ given that $f(4)=3$ and $f^{\prime}(4)=2$.

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 4, Problem 49

Instant Answer

Solved by Expert R M

06/07/2020

Step 1

We are asked to find the linear approximation of $f(3.85)$. Show more…

Show all steps

Thanks for your feedback!

Linear approximation Estimate $f(3.85)$ given that $f(4)=3$ and $f^{\prime}(4)=2$.

Play audio

Feedback

R M and 71 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Linear Approximation

Linear approximation is a technique used to estimate the value of a function near a point where the function's value and derivative are known. It relies on the assumption that the function behaves approximately like a straight line (its tangent) in the vicinity of that point.

Tangent Line

The tangent line to a function at a given point is the straight line that just touches the function at that point and has the same slope as the function does there. The equation of the tangent line serves as a linear model that approximates the function's behavior near the point of tangency.

Derivative

The derivative at a point provides the slope of the tangent line to the function at that point, indicating the instantaneous rate of change. This concept is fundamental in linear approximation, as it determines how small changes in the input affect the output of the function.

Please give Ace some feedback