# MAT135H1 Lecture Notes - Lecture 2: Maxima And Minima

34 views1 pages

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

fx x x x

=−+, 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