Unit 2

Unit 2

1. Partial Derivatives

   • Limit Defintion
   • Example

2. Local Linearity

   • The equation of a plane that is tangent to a point on a graph

3. Gradient

   • The Gradient is a Vector!!
   • Perpendicular to the Contour
     • Gradf is Large When Contours are Close Together
     • Points Uphill

4. The Chain Rule

   • Shows what variables depend on eachother
   • Make a Tree
     • Multiply Left Branch Partials by Right Branch Partials

5. Second Derivatives

   • Interpreting
     • f'(x)= Slope of Tangent f''(x)= Concavity

6. Extrema

   • Local Extrema
     • Finding Critical Points
       • Take the partials, set equal to zero
       • Discriminant
         • Tells you what kind of critical point it is
         • Interpreting Discriminant
   • Global Extrema
     • Where is the Global Max/Min?
       • At a Critical Point
       • On the Boundary

7. Velocity and Acceleration

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