Q. 134.0( 17 Votes )
On which of the following intervals is the function f given by f (x) = x100 + sin x –1 strictly decreasing?
A. (0,1)
B. 
C. 
D. None of these
Answer :
It is given that f (x) = x100 + sin x –1
Then, f’(x) = 100x99 + cosx
In interval (0,1), cos x >0 and 100x99 > 0
⇒ f’(x)>0
Therefore, function f is strictly increasing in interval (0,1).
In interval
, cos x < 0 and 100x99 > 0.
Also, 100x99 > cos x
⇒ f’(x) > 0 in 
Therefore, function f is strictly increasing in interval 
.
In interval 
, cos x < 0 and 100x99 > 0.
Also, 100x99 > cos x
⇒ f’(x) > 0 on 
Therefore, function f is strictly increasing in interval 
.
Hence, function f is strictly decreasing on none of the intervals.
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