RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 34 of Exercise 17.2

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34

Show that f(x) = – x sin x is an increasing function on (0, π/2) ?

We have,

f(x) = – x sinx


f ’(x) = 2x – sin x – x cos x


Now,


x ()


0 sin x 1, 0 cos x 1,


2x–sin x –x cos x > 0


f ’(x) ≥ 0


Hence,f(x) is an increasing function on ().


Chapter Exercises

More Exercise Questions

26

Find the interval in which is increasing or decreasing ?