HOW TO FIND ABSOLUTE MAX AND MIN FROM A GRAPH

Find the

a) Coordinates of the absolute maximum point.

b) Value of the absolute maximum

c) Coordinates of the absolute minimum point

d) Value of the absolute minimum

Problem 1 :

Solution :

a) Coordinates of the absolute maximum point. (2,2)

b) Value of the absolute maximum: absolute maximum value is 𝑓(𝑥) = 2 which occurs when 𝑥 = 2

c) Coordinates of the absolute minimum point (0, −2)

d)  Value of the absolute minimum : absolute minimum value is 𝑓(𝑥) = −2 which occurs when 𝑥 = 0

Problem 2 :

Solution :

a) Coordinates of the absolute maximum point is (3, 4)

b) absolute maximum value is 𝑓(𝑥) = 4 which occurs when 𝑥 = 3

c) Coordinates of the absolute minimum point is (8, -21)

d) Absolute minimum value is 𝑓(𝑥) = -21 which occurs when 𝑥 = 8

Problem 3 :

Solution :

a) Coordinates of the absolute maximum point is (0, 20)

b) absolute maximum value is 𝑓(𝑥) = 20 which occurs when 𝑥 = 0

c) Coordinates of the absolute minimum point is (-3, -60)

d) Absolute minimum value is 𝑓(𝑥) = -60 which occurs when 𝑥 = -3

Problem 4 :

Solution :

a) Coordinates of the absolute maximum point is (9, 40)

b) absolute maximum value is 𝑓(𝑥) = 40 which occurs when 𝑥 = 9

c) Coordinates of the absolute minimum point is (3, 4)

d) Absolute minimum value is 𝑓(𝑥) = 4 which occurs when 𝑥 = 3

Problem 5 :

Solution :

a) Coordinates of the absolute maximum point is (4, 53)

b) absolute maximum value is 𝑓(𝑥) = 53 which occurs when 𝑥 = 4

c) Coordinates of the absolute minimum point is (0, 20)

d) Absolute minimum value is 𝑓(𝑥) = 20 which occurs when 𝑥 = 0

Find the absolute maximum and absolute minimum

Problem 6 :

Solution :

• Absolute maximum is at (1, 1). 
• Absolute minimum is at (-5, -35)
• Absolute maximum value is y = 1
• Absolute minimum value is y = -35

Problem 7 :

Solution :

• Absolute maximum is at (4, 34). 
• Absolute minimum is at (-3, -15)
• Absolute maximum value is y = 34
• Absolute minimum value is y = -15

Problem 8 :

Find the following in the figure following.

a) Relative Max: ___

b) Relative Min: _____

c) Absolute Max: ____

d) Absolute Min:____

Solution :

a) Relative maximum is at (1, 5)

b) No relative minimum.

c) Absolute maximum is at x = 1 and maximum value is 5.

d) No absolute minimum.

Problem 9 :

a) Relative Max: ________

b) Relative Min: _________

c) Absolute Max: ________

d) Absolute Min: _________

e) Y-intercept: ___________

f) Zeros:

Solution :

a) At (-2, -3) the curve changes its direction from decreasing to increasing. So, relative minimum is at (-2, -3).

b) At (1, 1) the curve changes its direction from increasing to decreasing. So, the relative maximum is at (1, 1)

c) Absolute maximum is at x = 1, maximum value is y = 1

d) Absolute minimum is at x = -2, minimum value is y = -3

e) The curve intersects the y-axis at (0, 0). So, the y-intercept is 0.

f) The curve is intersecting at the x-axis, x = -3.2, 0 and 2.