How do you find the linear approximation #f(x)=2/x#, #x_0=1#?
1 Answer
An equation of a tangent line is a linear approximation.
Explanation:
The at a chosen value of
The tangent line through
The linear equation can be thought of as an equation for the tangent line or as a linear function giving an approximation of
The point-slope form of the equation of the tangent line (the line through
The linear approximation for
For
The linear approximation is
which you may prefer to write as
Here is a graph showing both. You can zoom in and out and drag the graph around the window. When you navigate away from this answer and return, the graph will start n the same position it has now.
graph{(y-2/x)(y+2x-4)=0 [-0.58, 2.458, 1.252, 2.771]}