MAT135H1 Lecture Notes - Lecture 2: Maxima And Minima

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Published on 22 Sep 2020
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4.2 Critical Points, Local Maxima, and Local Minima
Recall from Chapter 3, when we set
'( ) 0
fx
=
and solve for ‘x’, we determine critical points which could be
a local maximum value or local minimum value of
()
fx
The ‘x’ value of the critical points are called __________________________________
First Derivative Test:
o Used to check if a critical point is a local max or local min
o If
'( )
fx
changes from _____________________ to _______________________ at ‘c’, then the
critical point is a local _______________ of
()
fx
o If
'( )
fx
changes from _____________________ to _______________________ at ‘c’, then the
critical point is a local _______________ of
()
fx
o If
'( )
fx
does not change sign at ‘c’, then the critical point is neither a local max nor min
Example 1: Given
43 2
( ) 8 18
=+, determine the critical points and determine if it is a local maximum or local
minimum. Sketch the graph.
Homework: pg 178-180 #1, 2, 3ab, 5, 7abc, 8, 9, 10
critical number
fxincreasing f
Cx decreasing
Max I
fix decreasing and increasing
t
min pg
fx4324 236
04324 236 factortable
O4x Xtext 9KO axes
o4xCx 3Cx sI
dto ft
IT f1cx t
fxdear incr incr
crl fooYso31865 neither
o17load him or
at min
f334833t18135 xoat x
81 216 t16 Ifn
at EI i'Inumaximi
localmin
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