Gradients and Directional Derivatives, Part 2

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• Misc
  • Colloquium
    • “Perpetual Pest Control in the Face of Resistance Evolution?”
    • Dr. John Ringland, University at Buffalo
    • Thursday, Oct. 29, 4:00 PM
    • Newton 202
    • Extra credit
  • Hour exam 2 moved to Monday Nov. 2
• Questions?
  • Question 4, partial derivatives problem set?
    • Find dx/dz if xz + y lnx - x² + 4 = 0
    • Implicit differentiation
    • Differentiate both sides wrt z, treating x as function of z
    • Isolate dx/dz terms
    • Or use shortcut from section 14.4
• Directional Derivatives and Gradients
  • Lingering questions
    • Example 1?
      • Key idea is to substitute x₀+su₁ and y₀+su₂ into definition of f for x and y
  • Example
    • Find gradient and directional derivatives in various directions of f(x,y) = xy² - yx²; evaluate at (x,y) = (1,1)
      
    • Directional derivative gives instantaneous rate of change as you move in a certain direction
• Next
  • Tangent planes
  • Read section 14.6

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