# MA 227 Standard S06

Linearization

At the end of the course, each student should be able to…

• S06: Lineariz. Compute the linearization of a two-variable real-valued function at a point and use it for approximation.

## S06: Linearization

• Differentiable functions $$f(x,y)$$ may be approximated near a point $$P_0$$ by the linearization $$L(x,y)$$ defined by the tangent plane at that point.
• Its equation is $$L(x,y)=f(P_0)+f_x(P_0)(x-x_0)+f_y(P_0)(y-y_0)$$.
• Thus if $$<x,y>\approx P_0$$, then $$L(x,y)\approx f(x,y)$$.

### Textbook References

• University Calculus: Early Transcendentals (3rd Ed)
• 13.6 (exercises 25-30)