If the function and the derivative of the function `f(x)` is everywhere continuous and is given by
`f(x)={:{(bx^(2)+ax+4", for " x ge -1),(ax^(2)+b", for " x lt -1):}`, then

If the derivative of the function f(x) is every where continuous and is given by f(x)={{:(bx^(2)+ax+4,,, x ge 1), (ax^(2)+b, ,, x lt -1):}, then : a)a = 2, b = -3 b)a = 3, b = 2 c)a = -2, b = -3 d)a = -3, b= -2

Disucss the continuity of the function f given by f (x) = {:{ (-x, if x ge0) , (-x^(2) , if x lt 0):}

Find the cofficients a and b such that the following function f is continuous and differentiable at x=+-1: f(x)={{:((1)/(|x|)," when "|x|ge1),(ax^(2)+b," when " |x|lt1):}

If a function is everywhere continuous and differentiable such that f'(x)ge6 for all x in [2,4]andf(2)=-4, then

Suppose f(x) = {{:(a+bx "," x lt 1),(4 "," " "x=1),(b-ax "," x gt 1):}

The function f(x)= {(2 ax ", " x ge 3 ),( 3x +1 ", " x gt 3):} continuous at x= 3, then a =?

Discuss the continuity of the function f given by {{:(x," if "x ge 0),(x^2," if "x lt 0):} .