In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
From the graph of \(f\) in Figure \(\PageIndex{7}\), we see that f has an absolute maximum at \(x=1\) and an absolute minimum at \(x=−1.\) Hence, \(f\) has a local maximum at \(x=1\) and a local minim...From the graph of \(f\) in Figure \(\PageIndex{7}\), we see that f has an absolute maximum at \(x=1\) and an absolute minimum at \(x=−1.\) Hence, \(f\) has a local maximum at \(x=1\) and a local minimum at \(x=−1\). (Note that if \(f\) has an absolute extremum over an interval \(I\) at a point \(c\) that is not an endpoint of \(I\), then \(f\) has a local extremum at \(c.)\)
