RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 8 of Exercise 17.1

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8

Without using the derivative, show that the function f(x) = | x | is

A. strictly increasing in (0, ∞)


B. strictly decreasing in (-∞, 0).

We have,

f(x) = |x| =


(a)Let , (0,) and



So, f(x) is increasing in (0,)


(b) Let , (-∞, 0)and




f(x) is strictly decreasing on(-∞, 0).


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