Page 60 - Mathematics Class - XII

2. Plotting these points on the chart paper and joining the points by a free hand curve, the curve obtained is
shown in Fig. (b).

Fig. (b)

OBSERVATION
1. The absolute maximum value of f (x) is 20 at x = –2.

2. The absolute minimum value of f (x) is –7 at x = 1.

CONCLUSION
The above activity explains the concepts of absolute maximum and absolute minimum values of a function in a
given closed interval through its graph.

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

Knowledge Booster
We can find local maximum and local minimum by using first derivative, As, Consider f (x) = 2x + 3x –12x
3
2
f ′(x) = 6x + 6x – 12 = 0 gives the values of x as 1 and –2
2
Both these values of x lie in the given closed interval [–2, 2].
The function has local minimum at x = 1 and local maximum at x = – 2.

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