ITT Technical Institute
Framingham, Massachusetts
Quarter 7 Electronics Calculus
Instructor: Paul Burney

Name __________________________________

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Implicit Differentiation and Anti Derivatives
(Test #4)

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Useful Formulas:

Instructions:

Please solve the following problems. Credit will be given for work completed so make sure to show it!

 

1. Find the following derivatives using implicit differentiation. (20 points each).
   
   
   
   1. 12x + 3y = 0
      
      
      
      
      
      
      
      
      
      
   2. 5x² + 6y² = 163
      
      
      
      
      
      
      
      
      
      
2. Find the following anti-derivatives. (10 points each)
   
   
   
   1. Ä(x) = 8
      
      
      
      
      
   2. Ä(x) = 6x
      
      
      
      
      
   3. Ä(x) = 12 - 3x²
      
      
      
      
      
   4. Ä(x) = x^-5 + 3x^-2
      
      
      
      
      
   5. Ä(x) = 0.65x^1.5 - 3
      
      
      
      
      

BONUS QUESTION: 10 points

Describe how using derivatives makes it possible to solve maximum/minimum problems. Use graphs if helpful to your argument.