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Let f : [ 0, oo) to [ 0,3] be a function...

Let `f : [ 0, oo) to [ 0,3]` be a function defined by
`f(x) = {{:(max { sin t : 0 le t le x}" , " 0 le x le pi),( 2 + cos x", " x gt pi ):}`
Then which of the following is true ?

A

f is not continuous exactly at two points in `(0,oo)`

B

f is continuous everywhere but not differentiable exactly at two points in `(0,oo)`

C

f is differentiable everywhere in `(0,oo)`

D

f is continuous everywhere but not differentiable exactly atone point in `(0,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C
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