text: # Homework Help: Vector Analysis ifferential Calculus
  
  1. Aug 28, 2008
  
  ### Benzoate
  
  Vector Analysis:Differential Calculus
  
  1. The problem statement, all variables and given/known data
  
  The height of a certain hill(in feet) is given by
  
  h(x,y)=10(2xy-3x^2-4y^2-18x+28y+12)
  
  where y is the distance (in miles) north, x the distance east of South Hadley
  
  a)Where is the top of the hill located
  
  b) How high is the hill?
  
  2. Relevant equations
  
  grad T=dT/dx xhat+dT/dy yhat+ dT/dz zhat
  
  3. The attempt at a solution
  
  a) I need to find the distance in the x direction , so I would take the derivative of h(x,y) with respect to x
  
  dh/dx=20*x-12=0=> x=3/5 feet
  
  b) same algorithm, only I am now ask to calculate how high the hill is and so I would take the derivative of h(x,y) with respect to y:
  
  dh/dy=y=3*x+9=3*(.6)+9=10.8 feet
  
  or maybe I should calculate h(x,y) in order to determine the height of the hill. Therefore , I'd plugged x and y into h(x,y) right?
  
  Last edited: Aug 28, 2008
  2. Aug 29, 2008
  
  ### tiny-tim
  
  Hi Benzoate!
  
  (have a curly d: ∂ )
  Nooo …
  
  Your ∂h/∂x and ∂h/∂x are completely wrong …
  
  and what happened to all the other terms (and all the other 10s)?
  
  You need to go back to your book and look again at how to do partial derivatives …
  
  3. Aug 29, 2008
  
  ### Benzoate
  
  Re: Vector Analysis:Differential Calculus
  
  wow I messed up big time with calculating my partial derivatives.
  
  Anyway, dh/dx= 20y-90x-180= and dh/dy= 20x-80y+280 =0. once I calculate my values for x and y , I would be able to calculate the height which is h(x,y), correct?
  
  4. Aug 29, 2008
  
  ### tiny-tim
  
  (what happened to that ∂ I gave you? )
  
  erm … 90x is wrong
  
  and the equations would be a lot more manageable if you'd divided them by 20
  That's right!
  
  5. Aug 29, 2008
  
  ### HallsofIvy
  
  Re: Vector Analysis:Differential Calculus
  
  Why is this listed under "physics" rather than "mathematics"?
  
  6. Aug 29, 2008
  
  ### Benzoate
  
  Re: Vector Analysis:Differential Calculus
  
  well because the problem came from my intro to Electrodynamics textbook
  
  7. Aug 30, 2008
  
  ### tiny-tim
  
  it's field theory …
  
  The hill was part of a field!
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