Q7 of 105 Page 17

Show that is neither increasing nor decreasing on R.

We have,


Case 1


When x [0,)


Let >


⇒


⇒


⇒


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.


More from this chapter

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5

Show that is a decreasing function on (0, ∞).

 6

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

 8

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

A. strictly increasing in (0, ∞)


B. strictly decreasing in (-∞, 0).

 9

Without using the derivative show that the function f(x) = 7x - 3 is strictly increasing function on R.