Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you show that the linearization of #f(x) = (1+x)^k# at x=0 is #L(x) = 1+kx#?

1 Answer

May 22, 2016

Note that #f(0)=(1+0)^k=1#.

Assuming #k# is a constant, we see that #f'(x)=k(1+x)^(k-1)#. Thus #f'(0)=k(1+0)^(k-1)=k*1=k#.

Using the point #(0,1)# and slope of #k# we can write the linearization function: #L(x)=k(x+0)+1=1+kx#.

Related questions

See all questions in Introduction

Impact of this question

20519 views around the world

You can reuse this answer
Creative Commons License