If `f(x)={{:(-x^(2),,x >=0),((a^(2)-2a)+(b^(2)-2)x,,x < 0):} ` and `x=0` is point of maxima, then `a=`

f(x)=x^(2)-2x+2,x in[0,2]

Let f(x) = {{:(min{x, x^(2)}, x >= 0),(max{2x, x^(2)-1}, x (A) f(x) is continuous at x=0 (B) f(x) is differentiable at x=1 (C) f(x) is not differentiable at exactly three point (D) f(x) is every where continuous

If f(x)={{:(e^(2x^(2)+x),":",xgt0),(ax+b,":",xle0):} is differentiable at x=0 , then

If f(x) = {:(a^(2)sin^(2)x+e^(2) cos^(2)x", if " x le 0 ),(=e^(ax+b)", if " x gt 0):} is continuous at x = 0 , then b = …..

Let f(x) =|{:(secx,x^(2),x),(2sinx,x^(3),2x^(2)),(tan3x,x^(2),x):}|lim_(x to 0)f(x)/(x^(4)) is equal to

If quad f(x)={x^(2)-2x+3;x in(-2,0)x^(3)-x^(2)+2;x in[0,2]3-2x;x in(2,6), then

Consider f(x)={{:(-2",",-1lexlt0),(x^(2)-2",",0lexle2):} and g(x)=|f(x)|+f(|x|) . Then, in the interval (-2, 2), g(x) is