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Applied Calculus (MAT 121) Dr. Day, Thursday, April 12, 2012

Applied Calculus (MAT 121) Dr. Day, Thursday, April 12, 2012. Chapter 8: Multi-Variable Calculus!. Multi-Variable Functions. Big Ideas What are multi-variable functions? What new notation is there to learn?

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Applied Calculus (MAT 121) Dr. Day, Thursday, April 12, 2012

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  1. Applied Calculus (MAT 121)Dr. Day, Thursday, April 12, 2012 Chapter 8: Multi-Variable Calculus! MAT 121

  2. MAT 121

  3. Multi-Variable Functions Big Ideas • What are multi-variable functions? What new notation is there to learn? • How do we determine derivatives of multi-variable functions? What symbols and names are associated with multi-variable derivatives? • How do we explore extreme values of multi-variable functions? • What is the method of LaGrange Multipliers? How do we use it? MAT 121

  4. Review: Calculating Derivatives MAT 121

  5. Derivatives of Multi-Variable Functions • Limitations: Fix x as constant or fix y as constant. Look at graphical representations. • Example: MAT 121

  6. Applications The monthly profit (in dollars) of Bond and Barker Department Store depends on the level of inventory x (in thousands of dollars) and the floor space y (in thousands of square feet) available for display of the merchandise, as given by the equation: P(x,y) = -0.02x2-19y2+xy+24x+36y-20000 (a) Compute  ∂P∂x and  ∂P∂y when x = 4,000 and y = 15. (b) Repeat with x = 5,000 and y = 150. MAT 121

  7. Assignments WebAssign 8.1 due tonight! Chapter 8 Worksheet collected in class today. MAT 121

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