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Let f be function f(x)=cosx-(1-X^(2)/(2)...

Let f be function `f(x)=cosx-(1-X^(2)/(2))`.Then

A

f (x)is an increasing function

B

f (x) is decreasing function

C

`f (x)` is an increasing function in the interval `-oo lt x le 0` and decreasing in the interval `0 le x lt oo`

D

`f (x)` is a decreasing function in the interval `- oo lt x le 0` and increasing in the interval `0 le x lt oo`

Text Solution

Verified by Experts

The correct Answer is:
D
f(x) = - sin x +x , we know sin x `lt x ` for `x gt 0` and sin `x gt x ` for `x lt 0`
Thus f(x) `gt ` 0 (inc ) for x `gt 0` and f(x) `lt 0` for x `lt0` (dec)
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