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

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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