Page 53 - Mathematics Class - XII

Unit 1 TOPIC - 4: Application of Derivatives

ACTIVITY 4.1

OBJECTIVE
To understand the concepts of decreasing and increasing functions.

MATERIAL REQUIRED
Y A piece of cardboard or Y White paper Y Trigonometric tables
drawing board Y Sketch pen Y Scientific calculator

Y Wires/threads of different lengths Y Glue stick

PRE-REQUISITE KNOWLEDGE
1. Knowledge of the concept of increasing function.
2. Knowledge of the concept of decreasing function.

PROCEDURE
1. Take a piece of cardboard and paste a white paper on it.

2. Take two wires of convenient size and fix them on the white paper pasted on the plywood to represent
x-axis and y-axis (Fig. (a)).

3. Take two more pieces of wire each of suitable length and bend them in the shape of curves representing
two functions and fix them on the paper as shown in Fig. (b).

4. Take two straight wires each of suitable length for the purpose of showing tangents to the curves at
different points on them.

Fig. (a) Fig. (b)

DEMONSTRATION
1. Take one straight wire and place it on the curve (on the left) such that it is tangent to the curve at the point
say P and making an angle a with the positive direction of x-axis.
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2. Here, a is an obtuse angle, so tan a is negative, i.e., the slope of the tangent at P (derivative of the
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function at P ) is negative.
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