Concept:Greatest Integer Function: (Floor function)The function f (x) = [x] is called the greatest integer function and means greatest integer less than or equal to x i.e [x] ? x.The domain of [x] is R and the range is I.Note:Any function is differentiable only if it is continuous.The floor function f(x) = ?x? is differentiable in every open interval between integers, (n, n + 1) for any integer n.Calculation:Given that,y = [x + 1], -4 < x < -3We have to determine the derivative at y = [x + 1] at x = -3.5We know that the floor function is differentiable at all points except integer points.Hence, y = [x + 1] is differentiable at x = -3.5? y = [-3.5 + 1] = [-2.5] = -3? dy/dx = 0? The derivative of y with respect to x at x = -3.5 is 0.