The table below contains certain values of a function f and its derivative. Assume that the graph of f is nice and smooth and doesn't have any cusps or discontinuities; f"(r) exists everywhere. 0|1| 2 3 f(x) f'(z) 2 0.25 0.6 1 4.5 8 -4 -2 0.5 2 3.5 6.5 (a) "(3r – 1) dr (b) - 1) f"(r) dr

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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: