The graph of y=f(x) is shown. Define the function g(x) by: (see picture). Note that f(x) and g(x) are different functions. Use the given information to answer the following: a) f'(7.5)= b) f'(4)= c) g'(4)= d) g(10)-g(6)= e)True or false: g(2)>g(0) f) On the interval (0,12) what are the critical numbers of the function g?

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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: