Chapter Three, Differential Mean Value Theorem and Application of Derivatives

Knowledge logic structure diagram

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Postgraduate exam content

Differential median value theorem, Lupida's rule, the difference of function monotonicity (using derivative), the extreme value of function (judgment of extreme value: define the first-order decentered neighborhood to be derivable and the left and right neighborhood derivatives have different signs, and the second-order may be Derivation and the first-order derivative of this point is zero), the unevenness of the function graph (proof), the inflection point and the asymptote (solving steps: vertical asymptote, horizontal asymptote, oblique asymptote), the description of the function graph, The maximum and minimum values of the function, the arc differential, the concept of curvature, the radius of curvature.

Postgraduate exam requirements

1. Understand and use Rolle's Theorem, Lagrange's Mean Value Theorem and Taylor's Theorem (expansion of typical functions), understand and use Cauchy's Mean Value Theorem.
2. Master the method of finding the limit of an indeterminate formula by using the Law of Pittsburgh.
3. Understand the concept of the extreme value of a function, master the use of derivatives to judge the monotonicity of a function and the method of finding the extreme value of a function (first-order derivation point, second-order derivation), master the method of finding the maximum and minimum value of a function and its simple application.
4. Can judge the unevenness of the function graph by the derivative, find the inflection point and the horizontal, vertical and oblique asymptotes of the function graph, and draw the graph of the function.
5. Understand the concepts of curvature and radius of curvature, and be able to calculate curvature and radius of curvature.