Q8 of 105 Page 17

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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