Page 59 - Mathematics Class - XII

ACTIVITY 4.3

OBJECTIVE

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

MATERIAL REQUIRED

Y A piece of cardboard or Y Wires Y Graph paper Y Geometry box
drawing board Y White paper Y Glue stick

PRE-REQUISITE KNOWLEDGE
1. Knowledge of the concept of maximum value of a function.
2. Knowledge of the concept of minimum value of a function.
3. Knowledge of the concept of intervals of a function.

PROCEDURE
1. Fix a white chart paper of convenient size on a drawing board / cardboard using adhesive and paste a graph
paper on it.
2. Draw two perpendicular lines on the graph paper as the two rectangular axes.

3. Graduate the two axes as shown in Fig.(a).

Fig. (a)
4. Let the given function be f (x) = 2x + 3x – 12x in the interval [–2, 2].
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5. Taking different values of x in [– 2, 2], find the values of f (x) and plot the ordered pairs (x, f (x)).
6. Obtain the graph of the function by joining the plotted points by a free hand curve as shown in Fig. (b).

DEMONSTRATION
1. Some ordered pairs satisfying f (x) are as follows:

x – 2 – 1. 5 – 1 – 0.5 0 0.5 1 1.5 2

f (x) 20 18 13 6.5 0 – 5 – 7 – 4.5 4

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