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.
At x=0 the function is not defined so it makes no sense to ask if they are differentiable there. To be differentiable at a certain point, the function must first of all be defined there! As we head towards x = 0 the function moves up and down faster and faster, so we cannot find a value it is heading towards.