What two conditions must be met?
find the value of the constants a and b to ensure the following function is differentiable for all real values of x:
f(x) = { (ax / sqrtx) + b , x less than or equal to 1
and x^2 - 1 , x is greater than 1
also find a and subsequently the limit of lim (x->-2)[ 3x^2 + ax + a + 3/ x^2 + x - 2] which i found a to be 15 after some trial and error and established that the end result would be lim (x->-2) [(3x + 9)(x+2)/(x-1)(x+2)] = -1 but would like better reasoning for the deduction of a