Question

What is the linearization of f(x)=e^x at x=1?

Answer 1

Linearization is the approximation of the derivative of the function by a tangent line at a particular point.

f(x)=e^x
f'(x)=e^x
at x=1, f'(1)=e
So the tangent of slope "e" passes through the point (1,e).
The equation of the tangent line is therefore
(y-e)=e(x-1)
y=e*x-e+e
=e*x

See figure at the link below, and note that the line y=e*x passes through the origin.

http://img607.imageshack.us/img607/4157/1291771397.png