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Let f(x)={{:((x+1)^(3),-2ltxle-1),(x^(2/...

Let `f(x)={{:((x+1)^(3),-2ltxle-1),(x^(2//3)-1,-1ltxle1),(-(x-1)^(2),1ltxlt2):}`. The total number of maxima and minima of f(x) is

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)={{:((x+1)^(3),-2ltxle-1),(x^(2//3)-1,-1ltxle1),(-(x-1)^(2),1ltxlt2):}`
Clearly f(x) is continuous.
`rArr" "f'(x)={(3(x+1)^(2),-2ltxlt-1),((2)/(3)xxx^(-1//3),-1ltxlt1-{0}),(-2(x-1),1ltxlt2):}`
Sign scheme of f'(x)

Critical point `-1,0,1`
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