Applications of differentiation in biology, economics, physics, etc.

Practice using derivatives in a variety of different fields.

Problem

The cost, in dollars, of producing x gallons of detergent is given by
space, C, left parenthesis, x, right parenthesis, equals, 350, plus, 20, x, minus, 0, point, 08, x, start superscript, 2, end superscript, plus, 0, point, 0004, x, start superscript, 3, end superscript.
What is a formula for the marginal cost function C, space, prime, left parenthesis, x, right parenthesis, question mark
To the nearest dollar sign, 0, point, 01, what is the marginal cost of producing the 101, start superscript, s, t, end superscript gallon of detergent?
space, C, space, prime, left parenthesis, 100, right parenthesis, equals, dollar sign, space
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
space, slash, g, a, l, l, o, n
To the nearest dollar sign, 0, point, 01, what is the actual cost of producing the 101, start superscript, s, t, end superscript gallon of detergent?
space, C, left parenthesis, 101, right parenthesis, minus, C, left parenthesis, 100, right parenthesis, equals, dollar sign, space
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4