If the function `f(x)={A x-B ,xlt=1 3x ,1

Consider the function f(x)={2x+3,xlt=1-x^2+6,x >1

Examine the continuity of the function f(x)={3x-2,\ \ \ xlt=0x+1,\ \ \ x >0 at x=0 . Also sketch the graph of this function.

The value of b for which the function f(x)={5x-4,0xlt=1 , 4x^2+3b x ,1< x <2 and continuous at x=1

Examine the continuity of the function f(x)=3x-2,xlt=0 , f(x)=x+1,x>0" at x=0 Also sketch the graph of this function.

Find the complete set of values of alpha for which the function f(x) = {(x+1,xlt1 alpha , x =1 , is strictly increasing x=1 x^(2)-x+3,xlt1

For what choice of a and b is the function f(x)={x^2,xlt=c and a x+b ,x > c is differentiable at x=c

The range of the function f(x)=|x-1|+|x-2|,-1lt=xlt=3, is [1,3] (b) [1,5] (c) [3,5] (d) none of these

Let a and b are real numbers such that the function f(x)={(-3ax^(2)-2, xlt1),(bx+a^(2),xge1):} is differentiable of all xepsilonR , then

Verify Rolles theorem for the function f(x)=x(x-3)^2,\ 0lt=xlt=3 .

Redefine the function f(x)=|x-2|+|2+x|,-3lt=xlt=3