RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 6 of Exercise 17.1

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Show that decreases in the interval [0, ∞) and increases in the interval (-∞, 0].

We have,

Case 1

When x [0,)

Let , (0,] and

f(x1)< f(x2)

f(x) is decreasing on[0,∞).

Case 2

When x (-,0]

Let >

f(x) is increasing on(-∞,0].

Thus, f(x) is neither increasing nor decreasing on R.

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