If the function `f (x)= {{:(e ^(2x) -1",","when " x le 0),(ax+ (bx^(2))/(2)",","when " xgt0):}` is differentiable at `x=0` then-

If the function f(x)={{:(2x+3",","when "xle1),(ax^(2)+bx",","when "xgt1):} is differentiable everywhere then show that f '(3) =-10

The function f(x) ={{:(e^(2x)-1,","x lt 0),(ax+(bx^2)/2-,","xlt0):} continuous and differentiable for

f(x)={{:(3-x",","when",x le0, ),( x^(2)",", "when",xgt0):} is discontinuous at x=0

f(x)={{:(2x",","when",x lt0, ),(2",", "when", x =2),(x^(2)",","when",xgt2):} is discontinuous at x=0

If the function f(x) = {((sin^(2)ax)/(x^(2))","," when "x != 0),(" k,"," when " x = 0):} is continuous at x = 0 then k = ?

For the function f(x)={{:(x+2", "xgt0),(x-2", "xlt0):}

f(x)={{:(-x",","when",x lt0, ),(1",", "when", x =0),(x",","when",xgt0):} is discontinuous at x = 0

If f(x) = {{:(-x, " when "x lt 0),(x^(2), " when "0 le x le 1),(x^(3) -x+1, " when " x gt 1):} then f is differentiable at

If f(x) = {{:(-x, " when "x lt 0),(x^(2), " when "0 le x le 1),(x^(3) -x+1, " when " x gt 1):} then f is differentiable at