Mathematics Lab Activity-08 Class XII

Mathematics Laboratory Activities on Applications of Derivatives for class XI Non-Medical students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 06 

applications of derivatives

Activity - 08

Objective

To understand the concept of absolute maximum and minimum values of a function in a given closed interval through its graph.

Material Required

Drawing board, white chart paper, adhesive, geometry box, pencil and eraser, sketch pens, ruler, calculator.

Procedure

1. Fix a white chart paper of convenient size on a drawing board using adhesive.

2. Draw two perpendicular lines on the squared paper as the two rectangular axis.

Graduate the two axis as shown in figure 8.1

3. Let the given function be f(x) = (4x² - 9)(x² - 1) in the interval [-2, 2].

4. Taking different values of x in [-2, 2], find the values of x and plot the ordered pairs (x, f(x)).

5. Obtain the graph of the function by joining the plotted points by a free hand curve as shown in the figure 8.1.

Figure 8.1

6. Some ordered pair satisfying f(x) are as follows.

X	0	土0.5	土1.0	1.25	1.27	土1.5	土2
f(x)	9	6	0	-1.55	-1.56	0	21

7. Plotting these points on the graph paper and joining the points by a free hand curve, the curve obtained is shown in the figure 8.1

Observations

1. The absolute maximum value of f(x) is 21 at x =  土2

2. Absolute minimum value of f(x) is -1.56 at x = 1.27

Result

Absolute minimum and  maximum values are different from local maxima and minima.

Applications

This activity is useful in explaining the concepts of absolute maximum and minimum value of a function graphically.

VIVA – VOICE

Q1. Define absolute maxima ?

Ans. Let f be a function defined on an interval I containing c, then f(c) is absolute maxima if 

f(c) ≥ f(x) ∀ x ∈ I.

Q2. Define absolute minima ?

Ans. Let f be a function defined on an interval I containing c, then f(c) is absolute minima if 

f(c) ≤ f(x) ∀ x ∈ I.

Q3. When a number c is said to critical point of function 'f' ?

Ans. When f'(c) = 0.

Q4. Are absolute maxima or minima are unique, if exist ?

Ans. Yes.

Q5. Is there any function which neither have maxima nor minima ?

Ans. Yes.

Q6. Give an example of a function which has neither absolute maxima nor absolute minima.

Ans. Following function neither have absolute maxima nor absolute minima.

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