Summary: Mathematics

Read the summary and the most important questions on Mathematics

• Economic functions

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• What is the price function?

  p(x)

• How do you find marginal costs?

  C'(x) 
  
  Derivative of the cost function 

• What is the break even point? How do you calculate it?

  Point where costs are covered with revenue
  
  Calculated:
  P(x)=0       ->   Where profit equals zero
  or
  C(x)=R(x)   ->  Where costs equal revenue

• What do the small and capital letters mean in the economic functions?

  The small letters in economics are always per unit 
  
  The capital letters are always in total

• Derivatives

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• What is the derivative of a fraction?

  
  (g'(x)*h(x)-h'(x)*g(x))/[(h(x))]^2 

• What is the derivative of a product? u(x)*v(x)

  u'(x)*v(x)+u(x)*v'(x) or g'(x)*h(x)+h'(x)*g(x)

• Curve discussion rational functions

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• How do you determine the domain of a rational function?

  1. Denominator= 0 
  2. Solve for x
  
  Domain= R\{}

• How do you determine the roots/zeros of a rational function?

  When fraction: 
  
  numerator=0 
  Denominator is different than 0

• Curve discussion

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• How do you know the curvature of the function from the second (and third) derivative?

  When f''(x) is positive >0 -> Then the function is convex (right-left)
  
  When f''(x) is negative <0 -> Then the function is concave (left-right)

• Elementary mathematical rules + power rules

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• What is the power rule to a^x+b^x

  a^x+b^x=(a+b)^x
  
  The same for both + and -