Chapter 7.2, Problem 11E

Interpretation Introduction

Interpretation:

To show that ${\text{V= ax}}^{\text{2}}{\text{+ 2bxy + cy}}^{\text{2}}$ is positive definite if and only if $\text{a>0}$ and ${\text{ac - b}}^{\text{2}}\text{> 0}$.

Concept Introduction:

Using second derivative test, the origin is local extrema if ${\text{ac - b}}^{\text{2}}\text{> 0}$ and local minimum if ${\text{V}}_{\text{x}}{\text{(0,0) = V}}_{\text{y}}\text{(0,0) = 0}$ for the origin to be a critical point and for ${\text{V}}_{\text{xx}}\text{(0,0) = 2a >0}$.