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Question

Given p 4 is a positive real. Let A be the area of the bounded region enclosed by the curves y = 1 - |1-x| and y = |2x-p|. Then which among the following best describes A?

A
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B
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C
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D
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Solution

The correct option is C

Option (c)

Case 1: 0<p1 The area formed is of a triangle with vertices (p3,p3).(p2,0) and (p, p). Thus, the area is p26 sq. units.

Case 2: 1 p 3The figures formed is a quadrilateral (p3,p3),(p2.0),(p+23,4p3) and (1, 1).Thus, the area formed is 1316×(p2)2

Case 3: 3 p 4The area formed is the image of case 1.

Area = (4p)26

Thus, min (A) = 0 at p = 4 and max (A) = 13 at p = 2. Hence, option (c) is the right answer.


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