Maxima and Minima
Finding the largest or smallest value of a function is a main use of the derivative. The method is short: locate the critical points, classify them with a derivative test, and, on a closed interval, compare with the endpoints.
Engineering Mathematics · topic
Maxima, minima and the mean value theorems
Critical points, first and second derivative tests, global extrema on closed intervals, increasing and decreasing functions, concavity and inflection; Rolle's theorem, Lagrange's mean value theorem and Cauchy's form with their exact hypotheses.
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Mean Value Theorems
The mean value theorems link the average rate of change of a function over an interval to its instantaneous rate at some interior point. They are the bridge between "the derivative is positive" and "the function increases", and they give quick error bounds.
Maxima, minima and the mean value theorems cheat sheets
One-page visual sheets for this topic, in the sheet library on the store. Previews are free; the full sheets come with the subject pack.