Let f(x) `=x^(3)-3x +2.` Examine the monotonicity of function at points x=0.1,2

Explanation

` f'(x) =x^(3) -3x+2`
` f'(x) =3(x^(2)-1)`
`(i) f'(0) =-3" "rArr " ""decreasing at " x=0`
`(ii) f'(1) =0`
also f'(x) is positive on left neighbourhood and f(x) I negative in right neighbourhood.
`rArr` neither increasing nor decreasing at x=1
`(iii) f'(2) =9" " rArr" ""increasing at " x=2`
Note Above method is applicable only for functions those are continuous at x=a`