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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6

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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