Determine if the following piecewise defined function is differentiable at x = 0. Зх - 5, x20 f(x) = x2. + 3x - 5, x<0 What is the right-hand derivative of the given function? f(0 + h) – f(0) lim (Type an integer or a simplified fraction.) %3D h h→0+ What is the left-hand derivative of the given function? f(0 + h) – f(0) lim (Type an integer or a simplified fraction.) h h→0- Is the given function differentiable at x = 0? O No O Yes

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A: Given function is

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: