A potter made a mud vessel, where the shape of the pot is based on f(x)=|x-3|+|x-2|, where f(x) represents the height of the pot.

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Question 1

When x > 4, What will be the height in terms of x ?

(a) x – 2

(b) x – 3

(c) 2x – 5

(d) 5 – 2x

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Question 2

Will the slope vary with x value?

(a) Yes

(b) No

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Question 3

What is dy/dx at x = 3

(a) 2

(b) –2

(c) Function is not differentiable

(d) 1

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Question 4

When the x value lies between (2, 3) then the function is

(a) 2x  – 5

(b) 5 – 2x

(c) 1

(d) 5

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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

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  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Question A potter made a mud vessel, where the shape of the pot is based on ๐‘“(๐‘ฅ)=|๐‘ฅโˆ’3|+|๐‘ฅโˆ’2|, where ๐‘“(๐‘ฅ) represents the height of the pot. ๐‘“(๐‘ฅ)=|๐‘ฅโˆ’3|+|๐‘ฅโˆ’2| = {โ–ˆ((๐‘ฅโˆ’3)+(๐‘ฅโˆ’2), ๐‘ฅ โ‰ฅ3@โˆ’(๐‘ฅโˆ’3)+(๐‘ฅโˆ’2), 2<๐‘ฅ<3@โˆ’(๐‘ฅโˆ’3)โˆ’(๐‘ฅโˆ’2), ๐‘ฅโ‰ค2)โ”ค = {โ–ˆ(2๐‘ฅ โˆ’5, ๐‘ฅ โ‰ฅ3@โˆ’๐‘ฅ+3+๐‘ฅโˆ’2, 2<๐‘ฅ<3@โˆ’๐‘ฅ+3โˆ’๐‘ฅ+2, ๐‘ฅโ‰ค2)โ”ค = {โ–ˆ(๐Ÿ๐’™ โˆ’๐Ÿ“, ๐’™ โ‰ฅ๐Ÿ‘@ ๐Ÿ, ๐Ÿ<๐’™<๐Ÿ‘@โˆ’๐Ÿ๐’™+๐Ÿ“, ๐’™โ‰ค๐Ÿ)โ”ค 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‘“(๐‘ฅ) = {โ–ˆ(๐Ÿ๐’™ โˆ’๐Ÿ“, ๐’™ โ‰ฅ๐Ÿ‘@ ๐Ÿ, ๐Ÿ<๐’™<๐Ÿ‘@โˆ’๐Ÿ๐’™+๐Ÿ“, ๐’™โ‰ค๐Ÿ)โ”ค For x > 4, f(x) = 2x โˆ’ 5 So, the correct answer is (c) Question 2 Will the slope vary with x value? (a) Yes (b) No ๐‘“(๐‘ฅ) = {โ–ˆ(๐Ÿ๐’™ โˆ’๐Ÿ“, ๐’™ โ‰ฅ๐Ÿ‘@ ๐Ÿ, ๐Ÿ<๐’™<๐Ÿ‘@โˆ’๐Ÿ๐’™+๐Ÿ“, ๐’™โ‰ค๐Ÿ)โ”ค Now, Slope = ๐‘“โ€ฒ(๐‘ฅ) = {โ–ˆ(๐Ÿ, ๐’™ โ‰ฅ๐Ÿ‘@ ๐ŸŽ, ๐Ÿ<๐’™<๐Ÿ‘@โˆ’๐Ÿ, ๐’™โ‰ค๐Ÿ)โ”ค Since Slope changes as value of x changes So, the correct answer is (a) Question 3 What is ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ at x = 3 (a) 2 (b) โ€“2 (c) Function is not differentiable (d) 1 ๐‘“โ€ฒ(๐‘ฅ) = {โ–ˆ(๐Ÿ, ๐’™ โ‰ฅ๐Ÿ‘@ ๐ŸŽ, ๐Ÿ<๐’™<๐Ÿ‘@โˆ’๐Ÿ, ๐’™โ‰ค๐Ÿ)โ”ค Since on left and right side of x = 3, value of ๐‘“โ€ฒ(๐‘ฅ) 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‘“(๐‘ฅ) = {โ–ˆ(๐Ÿ๐’™ โˆ’๐Ÿ“, ๐’™ โ‰ฅ๐Ÿ‘@ ๐Ÿ, ๐Ÿ<๐’™<๐Ÿ‘@โˆ’๐Ÿ๐’™+๐Ÿ“, ๐’™โ‰ค๐Ÿ)โ”ค 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)

About the Author

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Davneet Singh
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.