# Absolute maximum and the absolute minimum ```1.
Find the absolute maximum and the absolute minimum of f (x )  2x 2  6x  6 .
 3 3
Answer: Absolute minimum: f    ; no absolute maximum
 2 2
2.
Find the absolute maximum and the absolute minimum of f ( x)  4  x 2 / 3 .
Answer: Absolute maximum: f  0  4; no absolute minimum
3.
Find the absolute maximum and the absolute minimum of f ( x)  3x  4 .
Answer: No absolute maximum: no absolute minimum
4.
Find the absolute maximum and the absolute minimum of f ( x )  x 2  6 x  6 on   2,4 .
Answer: Absolute maximum: f   2  22; absolute minimum: f (3)  3
5.
Find the absolute maximum and the absolute minimum of f ( x)   x 2  2 x on  2, 2 .
Answer: Absolute maximum: f 1  1; absolute minimum: f (2)  8
6.
7.
Find the absolute maximum and the absolute minimum of f ( x)  2 x  6 on [0,5].
Answer: Absolute maximum (0,6): Absolute minimum (5, -4)
Find the absolute maximum and the absolute minimum of f ( x)  x3  3x 2 on  2,3 .
Answer: Absolute maximum: f  3  54; absolute minimum: f (0)  0
8.
Find the absolute maximum and the absolute minimum of g ( x) 
x2
on  4, 4 .
x2
Answer: Absolute maximum: none; absolute minimum: none
9.
Find the absolute maximum and the absolute minimum of g ( x ) 
x2
on   4,1 .
x2
1
Answer: Absolute maximum: g (4)  ; absolute minimum: g (1)  3
3
10.
Find the absolute maximum and the absolute minimum of f ( x)  3x 2/ 3  6 x  6 on 1,8 .
Answer: Absolute maximum: f 1  3; absolute minimum: f (8)  30
11.
x
on  4,8 .
x 4
1
1
Answer: Absolute maximum: f  2  ; absolute minimum: f ( 2)  
4
4
Find the absolute maximum and the absolute minimum of f ( x) 
2
1
on  2, 2 .
x  3x  4
1
 3 4
Answer: Absolute maximum: f     ; absolute minimum: f ( 2) 
 2 7
14
12.
Find the absolute maximum and the absolute minimum of f ( x) 
13.
Find the absolute maximum and the absolute minimum of f ( x) 
Answer: Absolute maximum: f  2 
14.
2
x
on  3,3 .
x  3x  4
2
1
; absolute minimum: f ( 2)  1
7
Given the graph of f, determine the absolute maximum and absolute minimum.
Answer: Absolute max: (0,3) ; Absolute min: none
15.
Given the graph of f, determine the absolute maximum and absolute minimum.
Answer: Absolute max: (1, 6) ; Absolute min: (3, 2)
16.
Given the graph of f, determine the absolute maximum and absolute minimum.
Answer: Absolute max: (2, 7) ; Absolute min: ( 3, 2)
17.
Given the graph of f, determine the absolute maximum and absolute minimum.
Answer: Absolute max: (3,9) ; Absolute min: (6, 0) and (0, 0)
18.
An arrow is shot from a cliff 100 feet above the ground. The height of the arrow above
the ground at any time t (measured in seconds) is given by h(t )  16t 2  320t  100
(with h measured in feet). Find the maximum height of the arrow above the ground.
19.
A company has determined that its profit (P) depends on the amount of money spent on
2x
advertising (x). The relationship is given by the equation P( x )  2
 70 , where P
x 4
and x are measured in thousands of dollars.
(a) What amount should the company spend on advertising to assure maximum profit?