How to Find Minimum Profits With Calculus

Calculus is an important tool in mathematics to help determine complex problems with variables. In addition, it is a way to understand different aspects from parabolic lines. This comes in handy when trying to determine the maximum and minimum profits possible for a business. In particular, minimum profits are important to know when you are calculating the minimum possible income you could receive under a certain circumstance.

Instructions

    • 1

      Determine your formula for revenue. This is determined by graphing the data over time. It could be seasonally, yearly or in any increment that you choose.

    • 2

      Find the graph of the line using the intercept points and the slope. Use the formula (y2 - y1) / (x2 - x1) to find the slope of the line. Assume that you have an exponential line fit for analysis with calculus in the form of f(x) = x^2 - 2x + 3.

    • 3

      Take the first derivative of the formula; that operation results in the new equation: f ' (x) = 2x - 2. Solve for x in the equation where x = 1.

    • 4

      Evaluate the equation when x is equal to 1: f(1) = 1^2 + 2(1) + 3 = 6. The minimum position of this line is (1, 6).

    • 5

      Take the second derivative of the equation and insert the value 1. If the result is positive, then the line slopes upward and can confirm it is a minimum at (1, 6).

      f ' (x) = 2x - 2

      f " (x) = 2

      f" (1) = 2

      The number 2 is positive, so it is confirmed.

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