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Which of the following statement is true...

Which of the following statement is true for the function `f(x)={{:(sqrt(x),","x ge 1),(x^(3) ,","0 le x lt 1),((x^(3))/(3)-4x,"," x lt 0):}`

A

It is monotonic increasing `AA x in R `

B

f'(x) fails to exist for 3 distinct real values of x

C

f'(x) changes its sign twice as x varies from `(-oo,oo)`

D

Function attains its extreme values at `x_(1) and x_(2)` , such that ` x_(1)x_(2) gt 0`

Text Solution

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The correct Answer is:
C
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