Class 12
APPLICATIONS OF DERIVATIVES
BY
Ganesan Govindaraj
Methods to find Maxima and Minima
There are two methods to find maxima and
minima for the given function 𝑓(𝑥)
Method 1: Without Using Derivative
Method 2: Using Derivative
i) First Order Derivative Test
ii) Second Order Derivative Test
Finding MAXIMA and MINIMA for the given curve.
Maximum and Minimum values are also called as Extreme values or Extremes.
1) Functions may have both Maximum value and Minimum value
3 POSSIBLITIES
2) Functions may have only Maximum value (OR) Minimum
OF FUNCTIONS
3) Functions may NOT have both Maximum value and
Minimum value
Two Types
of Extrema
Absolute Extreme Values
Local Extreme Values
( for Closed Interval )*
( for Open Interval )
Absolute Maximum
Absolute Minimum
Local Maximum
Local Minimum
(another name
(another name
(another name
(another name
Global Maximum )
Global Minimum )
Relative Maximum)
Relative Minimum)