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# Analyzing graphs and finding derivatives

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20. The graph below displays growth of a town's population y = P(t) over the next 3 years, where t is time in months.
a. Estimate how fast the population is increasing 5 months, and 20 months from now.
b. Graph y = P'(t).

In graphs of questions 2, 4 and 6, determine which is the f(x) function and which is the derivative?

https://brainmass.com/math/derivatives/analyzing-graphs-finding-derivatives-349797

#### Solution Preview

20. The rate of change in the value of the function with respect to a change in the value of x is the derivative of the function. The derivative at a point is the slope of the tangent line to the graph of y=f(x) at that point. So, to estimate the growth rate 5 and 20 months from now, we need to estimate the slopes of the tangent lines to the given graph at x=5 and x=20. The first one ...

#### Solution Summary

The process of analyzing the graph of a function to find its values and estimate the values of its derivative is illustrated with several examples. Examples of matching the graph f a function to the graph of its derivative are also given.

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