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

Let f(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 _________

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

If f(x)={(3x+2,xle0),(2-3x,xgt0):}

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

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