In this unit we show how differentiation can be used to find the maximum and minimum values of a function. Because the derivative provides information about
mc ty maxmin
All of these max and mins (local or absolute) are called Extreme Values. Some functions can have an absolute max and no absolute min (or vice versa). There are
maximum and minimum values
At the end of the last lecture we knew how to differentiate any polynomial function may be increasing
lecture
Absolute maxima are also local maxima etc. • Horizontal lines will have absolute maximum and minimim values equal: for example f(x) = 1 has absolute maximum
5 maj 2005 to use differentiation to find maxima and mininima of functions. ... all values of x this stationary point is a local minimum. Thus the.
PlymouthUniversity MathsandStats maxima and minima
Local Max. points and Max values: Local Min. points and Min values: Inflection points at: Concave Up in the intervals: Concave Down in the intervals:.
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The following diagram shows the graph of the derivative of . The graph of has a local minimum at A
IB Derivatives
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smallest value (locally) of a function occurs. We will also use derivative to find intervals on which a function is increasing or decreasing.
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f has a local minimum at c if f(c) is the smallest function value when x is near c. 3. Absolute maximum at s absolute minimum at r
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