If `f(x)={{:(ax^(2)+bx+2,,,xge2),(bx^(3)+2ax^(2),,,xlt2):}` is differentiable everywhere, then `(|a|+|b|)/(2)` is

If f(x)={{:(2x^(2)+3,,,xge3),(ax^(2)+bx+1,,,xle3):} is differentiable everywhere, then (a)/(b^(2)) is equal to

ax^(2)+bx+c

If function f(x)={{:(asqrt(x+7),,,0lexlt2),(bx+1,,,xge2):} is differentiable a ge 0 , then the 2a+4b is equal to

" If "f(x)={[sin2x,,-2<=x<=0],[ax+b,,0<=x<=2]" ,is differentiable everywhere in "(-2,2)," then "(a,b)" equals."

Let a and b are real numbers such that the function f(x)={(-3ax^(2)-2, xlt1),(bx+a^(2),xge1):} is differentiable of all xepsilonR , then

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

If the derivative of the function f(x)={{:(ax^(2)+b,xlt-1),(bx^(2)+ax+4,xge-1):} is every where continuous, then what are the values of a and b?

Find 'a' and 'b', if the function given by: f(x)={{:(ax^(2)+b", if "xlt1),(2x+1", if "xge1):} is differentiable at x = 1.