MAT135H1 Lecture 8: 3.2 Max and Min Values on an Interval

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Published on 22 Sep 2020
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3.2 Maximum and Minimum on an Interval (Extreme Values)
Calculus can be used to determine the maximum and minimum values of a function on an interval
The derivative at the maximum and minimum is equal to _________________
! i.e. the tangent is horizontal (slope of the tangent is _______________ )
Algorithm (steps) for Finding Maximum or Minimum (Extreme Values)
! For
()fx
on an interval [a, b]
1) Find the derivative,
'( )fx
2) Find all points in the interval [a, b] where
'( ) 0fx=
3) Evaluate
()fx
at the endpoints of the function [a, b], and points where
'( ) 0fx=
4) Compare the value is step 3:
o the largest value is the max value of
()fx
on the interval
o the smallest value is the min value of
()fx
on the interval
absolute
absolute absolute local
max
local
absolute min local
absolute min
absolute
zero
zero
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