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 \PageIndex7, 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 \PageIndex7, 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.)
