Capitalism is an economic system based on private ownership of the means of production and their operation for profit. Characteristics central to capitalism include private property, capital accumulation, wage labor, voluntary exchange, a price system, and competitive markets.
f(x) = (x+1)^1/2. Hi Carla, The derivative of $f(x)$ is the limit, as $h$ approaches zero of the difference quotient. \[\frac{f(x + h) - f(x)}{h}.\]. For your function this difference quotient is. \[\frac{(x + h + 1)^{1/2} - (x + 1)^{1/2}}{h}.\]. If you multiply the numerator and denominator by $(x + h + 1)^{1/2} + (x + 1)^{1/2}$ and simplify you will arrive at an expression that can be evaluated as $h$ approaches zero.
In other words, a function f is continuous at a point x=a, when (i) the function f is defined at a, (ii) the limit of f as x approaches a from the right-hand and left-hand limits exist and are equal, and (iii) the limit of f as x approaches a is equal to f(a). Before we go further, let's begin by constructing functions that are not continuous.