Like
Report
Numerade Educator
Problem 32 Medium Difficulty
Let $ f(x) = (x - 1)^2 g(x) = e^{-2x} $
and $ h(x) = 1 + \ln(1 -2x) $
(a) Find the linearization of $ f, g $ and $ h $ at $ a = 0. $ What do you notice? How do you explain what happened?
(b) Graph $ f, g, $ and $ h $ and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.
Answer
(a) SEE EXPLANATION
(b) If $x>0,$ then $f, g, h$ going from best to worst. If $x<0,$ then $h, f, g$ going
from best to worst. Please see graph
Discussion
You must be signed in to discuss.
Top Calculus 1 / AB Educators
Caleb E.
Baylor University
Kristen K.
University of Michigan - Ann Arbor
Michael J.
Idaho State University
Joseph L.
Boston College
Watch More Solved Questions in Chapter 3
Video Transcript
Okay. We know that because each part of X is native to over one plus two acts, you know h of zero is one, and hpe from zero is gonna be negative to. Therefore, we have one month's two acts. Recall the old three liberalizations are equivalent to each other because G prime of zero is the same as all the other variables. Promise here, As you can see, if X is greater than zero than F G and H go from best to worst. If X is less than zero after an edge or at h f G go from best to worst.
Top Calculus 1 / AB Educators
Caleb E.
Baylor University
Kristen K.
University of Michigan - Ann Arbor
Michael J.
Idaho State University
Joseph L.
Boston College
