Let `f(x)={:{(6","xle1),(7-x","xgt1):}` 'then for f(x) at x=1 discuss maxima and minima.

Is the function f defined by f(x)={(x", if "xle1),(5", if "xgt1):} continuous at x=0, at x=1 and at x=2 ?

Let f(x)={:{(x^(2)-1",",xle1),(-x^(2)-1",",xgt1.):} "Find"lim_(xrarr1)f(x).

The function f(x)={(2,xle1),(x,xgt1):} is not differentiable at

If f(x)={(x","xle1,),(x^2+bx+c",",xgt1):} then find the values of b and c if f(x) is diferentiable at x=1.

If f(x)={{:(2x^(2)+1",",xle1),(4x^(3)-1",",xgt1):} , then int_(0)^(2)f(x)dx is

Let f(x) = {(3 , ,xlt1),(4-x,,xgt1):}, Investigate x=1 for the existence of a local maxima/minima.

if f(x) = {{:(x+2",",xle1),(cx^(2)",",xgt-1):}, then find c when lim(xto-1)f(x) exists.

A function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(3-ax^(2),"for " xgt1):} If f (x) is continuous at x = 1 , find the value of a.