If f(x) =If `f(x)={:{(x^2+3x+a"," x le 1),( " "bx +2"," x gt 1):}` is defferentiable for all values of x, than find the values of 'a' and 'b'.

if f(x) = {{:(x^2, x le 1),(ax + b ,x gt 1):} is differentiable at x = 1 . Find the values of a and b.

If f (x) = {{:(x + 1 , x le 1), (3 - ax^(2) ,x gt 1):} is continuous at x =1, then the value of a is

Find lim_(x to 1) f(x) if f(x)={:{(x^2-1,x le1),(x^2+1, x gt1):}

If f(x) = {(2x+1,",",x le 1),(-3-kx^(2),",",x gt 1):} is continuous at x = 1, then the value of k is

If f(x) = {(2x+1,",",x le 1),(-3-kx^(2),",",x gt 1):} is continuous at x = 1, then the value of k is

Find the values of p and q, so that f(x) = {(x^(2) + 3x + p,x le 1),(qx + 2,x gt 1):} is differentiable at x=1.

If f(x)={:{(x,x le 1),(x^(2)+bx+c, x gt 1 and f'(x)) exists finitely for all x in R , then

If f (x) {{:( ax + 3"," , x le 2), ( a ^(2) x -1 "," , x gt2'):} then the values of a for which f is continuous for all x are

Let f(x) = {(x^(3) - x^(2) + 10x - 5",", x le 1),(-2x + log_(2)(b^(2) - 2)",",x gt 1):} find the values of b for which f(x) has the greatest value at x = 1.