Consider the function f(x) = 4x° 4x on the interval [ – 5, 5]. Find the average or mean slope of the - function on this interval. By the Mean Value Theorem, we know there exists at least one c in the open interval (- 5, 5) such that f'(c) is equal to this mean slope. For this problem, there are two values of c that work. The smaller one is and the larger one 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: