`Iff(x)={3x^2+12 x-1,-1lt=xlt=2 37-x ,2

If f(x)={(3x^2+12x-1,-1lexle2),(37-x,2ltxle3):}

If f(x)=3x^(2)+12x-1,-1lexle2,=37-x,2ltxle3 , then :

If f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):} then

If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x le 3):} , show that f(x) is increasing in [-1, 2]

If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x le 3):} , show that f(x) has maximum value at x = 2.

If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x le 3):} , show that f'(x) does not exist at x = 2

If f(x)={{:(3x^(2)+12x-1",",-1lexle2),(37-x",",2ltxle3):} , Then

If f(x)={(x^2)/2 , if 0lt=xlt=1 2x^2-3x+3/2 , if 1

Discuss the applicability of Rolles theorem on the function f(x)={(x^2+1 ,, if \ 0lt=xlt=1),(3-x ,,if 1ltxlt=2):}