Function for which LMVT is applicable bu...

Function for which LMVT is applicable but Rolle’s theorem is not

`f(x)=x^(3)-x, x in [ 0, 1]`

`f(x)={(x^(2)"," 0 le x lt 1),(x "," 1 lt x le 2):}`

`f(x)=e^(x), x in [-3, 3]`

`f(x)=1- root3 (x^(2)), x in [-1, 1]`

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Among the following, the function (s) on which LMVT theorem is applicable in the indecatd intervals is/are

`f(x)=x^((1)/(3))"in"[-1,1]`

`f(x)=x+1/x"in"[(1)/(2),3]`

`f(x)=(x-1)|(x-1)(x-2)|"in"[-1,1]`

`f(x)=e^(|(x-1)(x-3)|)"in"[1,3]`

`f(x)=x^((1)/(2)), x in [-2, 3]`

`f(x)=sinx,x in[-pi, (pi)/(6)]`

`f(x)=ln((x^(2)+ab)/(x(a+b))), x in [a, b], 0 lt a lt b`

`f(x)=e^(x^(2)-x), x in [0, 4]`

`f(x)=x^(2), x in [3, 4]`

`f(x)= ln x, x in [1, 3]`

`f(x)=4x^(2)-5x^(2)+x-2, x in [0,1]`

`f(x)={x^(4)(x-1)}^(1//5), x in [- 1/2 , 1/2]`