1.

Check monotonocity at following points for (i) f(x) =x^(3) -3x +1 =-1,2 (ii) f(x) +|x -1|+2|x-3|-|x+2| "at " x=-2,0,3,5 (iii) f(x) =x^(1//3) """at""" x=0 (iv) f(x)=x^(2) n +(1)/(x^(2)) """at""" x=1,2 (v) f(x) ={underset( 3 sin x , ""x ge0)(x^(3) +2x^(2) 5xgt 0)," at " x=0

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Answer :(i) Neither increasingnor decreasingat x=-1 and INCREASING at x=2
(ii) at x=-2 decreasing
at x=0 decreasing
at x=3 neitherincreasing nor decreasing
at x=5 increasing
(III) STRICTLY increasing at x=0
(IV) Strictly increasing at x=2 neither 1 nor D at x=1
(v) Strictly increasing at x=0


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