RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 33 of Exercise 17.2

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33

33 Prove that the function f(x) = cos x is :

i. strictly decreasing on (0, π)


ii. strictly increasing in (π, 2π)


iii. neither increasing nor decreasing in (0, 2 π)

Given f(x) =cos x


(i) Since for each x (),sin x > 0


⇒


So f is strictly decreasing in (0,)


(ii) Since for each x (),sin x <0


⇒


So f is strictly increasing in (,2)


(iii) Clearly from (1) and (2) above, f is neither increasing nor decreasing in (0,)


Chapter Exercises

Exercise 17.1
Exercise 17.2
MCQ

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32

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33

33 Prove that the function f(x) = cos x is :

i. strictly decreasing on (0, π)


ii. strictly increasing in (π, 2π)


iii. neither increasing nor decreasing in (0, 2 π)
34

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