# Linearise a function

Discussion in 'Homework Help' started by Peytonator, Mar 29, 2011.

1. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
3
Hi there,

How do I linearise the following function:

Vo = Vs - K(Vi - Vt)^2

around the point Vi

Thanks

Last edited: Mar 29, 2011
2. ### Papabravo Expert

Feb 24, 2006
10,138
1,789
The first derivative at the point Vi will be a linear approximation to the original quadratic function.

Peytonator likes this.
3. ### Georacer Moderator

Nov 25, 2009
5,142
1,266
Don't forget to actually build a line that will have the inclination of the tangent, but will also cross the point around which the linearization will take place.

4. ### Papabravo Expert

Feb 24, 2006
10,138
1,789
Right. I should have said that you:

Write the equation of the linearization using the point-slope method using the point Vi, and evaluating the first derivative at Vi for the slope to fix the intercept.

Some algebra and you have the equation of the line in slope-intercept form.

Of course this approximation is only valid in a delta-neighborhood of the point Vi.