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5.5. Plan a general study of the function

Lecture



The full research of the function is carried out according to the following plan:

  1. The scope of the function.
  2. Parity, oddness, periodicity of the function.
  3. The continuity of the function.
  4. Asymptotes.
  5. Zero functions and constancy intervals.
  6. Intervals of monotony and extremes.
  7. Convexity, concavity, points of inflection.
  8. Plotting.

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Lectures and tutorial on "Mathematical analysis. Differential calculus"

Terms: Mathematical analysis. Differential calculus

Indeterminate form
2.1. Real argument function
2.1. The concept of the limit of function
2.2. Equivalence of infinitesimal
2.3. Unilateral limits
2.4. Bound theorems
2.5. The first and second wonderful limits
3. Continuity of function 2.3.1. Continuous and discontinuous functions
3.2. Break points and their classification
2.4. Derivative 2.4.1. Derivative Definition
4.2. Basic rules for differentiation
4.3. Derivatives Table
4.4. Derivative of a parametrically given function
4.5. Differentiation of exponential-power function
2.5. General investigation of the function 2.5.1. Decreasing and increasing function
5.2. Function asymptotes
5.3. Extremum functions
5.4. Convexity, concavity and inflection points
5.5. Plan a general study of the function
2.6. Functions of many variables (FMP) 2.6.1. Scope of FMP
2.6.2. Partial derivatives
2.6.3. Full differential
2.6.4. Derivative of a complex function
2.6.5. Derivative of implicit function
2.6.6. Extremes FMP
2.6.7. Directional derivative, gradient
Examples of solving problems to the section limits and derivative. differential calculus
Zero to the power of zero