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

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

If f(x)={1+x, for 0lt=xlt=2 3-x, for 2lt x lt=3 then the number of values of x at which the function fof is not differentiable is 2 (b) 1 (c) 3 (d) 0

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lt=xlt=2 3-x ,2 2

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

if f(x)= {x^3+x^2,for 0lt=xlt=2x+2 ,for2

Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 ),(" "37 - x," "2 lt x le 3 ):} is continuous at x = 2

The relation f is defined by f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10 The relation g is defined by g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10 Show that f is a function and g is not a function.

The relation f is defined by f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10 The relating g is defined by g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10 Show that f is a function and g is not a function.

Evaluate: (i) \int_(-1)^1f(x)dx ,\where\, f(x)={1-2x ,xlt=0 ;1+2x ,xgt=0} , (ii)\ int_(-1)^4f(x)dx ,\where\, f(x)={2x+8,-1lt=xlt=2; 6x, 2lt=xlt=4}

if f(x)={x^3+x^2,for0lt=xlt=2x+2,for2