Question A potter made a mud vessel, where the shape of the pot is based on ๐(๐ฅ)=|๐ฅโ3|+|๐ฅโ2|, where ๐(๐ฅ) represents the height of the pot.
๐(๐ฅ)=|๐ฅโ3|+|๐ฅโ2|
= {โ((๐ฅโ3)+(๐ฅโ2), ๐ฅ โฅ3@โ(๐ฅโ3)+(๐ฅโ2), 2<๐ฅ<3@โ(๐ฅโ3)โ(๐ฅโ2), ๐ฅโค2)โค
= {โ(2๐ฅ โ5, ๐ฅ โฅ3@โ๐ฅ+3+๐ฅโ2, 2<๐ฅ<3@โ๐ฅ+3โ๐ฅ+2, ๐ฅโค2)โค
= {โ(๐๐ โ๐, ๐ โฅ๐@ ๐, ๐<๐<๐@โ๐๐+๐, ๐โค๐)โค
Question 1 When x > 4, What will be the height in terms of x ? (a) x โ 2 (b) x โ 3 (c) 2x โ 5 (d) 5 โ 2x
๐(๐ฅ) = {โ(๐๐ โ๐, ๐ โฅ๐@ ๐, ๐<๐<๐@โ๐๐+๐, ๐โค๐)โค
For x > 4,
f(x) = 2x โ 5
So, the correct answer is (c)
Question 2 Will the slope vary with x value? (a) Yes (b) No
๐(๐ฅ) = {โ(๐๐ โ๐, ๐ โฅ๐@ ๐, ๐<๐<๐@โ๐๐+๐, ๐โค๐)โค
Now,
Slope = ๐โฒ(๐ฅ)
= {โ(๐, ๐ โฅ๐@ ๐, ๐<๐<๐@โ๐, ๐โค๐)โค
Since Slope changes as value of x changes
So, the correct answer is (a)
Question 3 What is ๐๐ฆ/๐๐ฅ at x = 3 (a) 2 (b) โ2 (c) Function is not differentiable (d) 1
๐โฒ(๐ฅ) = {โ(๐, ๐ โฅ๐@ ๐, ๐<๐<๐@โ๐, ๐โค๐)โค
Since on left and right side of x = 3, value of ๐โฒ(๐ฅ) is different
It implies that the Function is not differentiable
So, the correct answer is (c)
Question 4 When the x value lies between (2, 3) then the function is (a) 2x โ 5 (b) 5 โ 2x (c) 1 (d) 5
๐(๐ฅ) = {โ(๐๐ โ๐, ๐ โฅ๐@ ๐, ๐<๐<๐@โ๐๐+๐, ๐โค๐)โค
For 2 < x < 3,
f(x) = 1
So, the correct answer is (c)
Question 5 If the potter is trying to make a pot using the function f(x) = [x], will he get a pot or not? Why? (a) Yes, because it is a continuous function (b) Yes, because it is not continuous (c) No, because it is a continuous function (d) No, because it is not continuous
f(x) = [x] = Greatest Integer Function
And, Greatest Integer Function is not continuous
So, the correct answer is (d)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.