If `f(x)={{:(3-x^(2)",",xle2),(sqrt(a+14)-|x-48|",",xgt2):}` and if f(x) has a local maxima at x = 2, then greatest value of a is

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

L e tf(x)={|x^2-3x|+a ,0lt=x<3/2-2x+3,xgeq3/2 If f(x) has a local maxima at x=3/2 , then greatest value of |4a| is _________

Let f:""RrarrR be defined by f(x)={(k-2x , if xle-1),( 2x+3, if x gt-1):} . If f has a local minimum at x""=""-1 , then a possible value of k is

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

A function f(x) = {:{(1+x",",xle2),(5-x,","xgt2):} is

If f(x) = {{:( 1+ x ,"for " xle 2),( 5-x,"for " xgt 2):},then

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

If the function defined by : f(x)={{:(2x-1", "xlt2),(a", "x=2),(x+1", "xgt2):} is continuous at x = 2, find the value of 'a'. Also discuss the continuity of f(x) at x = 3.

The function f(x)=(ax+b)/((x-1)(x-4)) has a local maxima at (2,-1), then

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