James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

4
Applications of Differentiation
When we view the world
around us, the light entering
the eye near the center of the
pupil is perceived brighter
than light entering closer to
the edges of the pupil. This
phenomenon, known as
the Stiles–Crawford effect, is
explored as the pupil changes
in radius in Exercise 80
on page 313.
© Tatiana Makotra / Shutterstock.com
We have already investigated some of the applications of derivatives, but now that we
know the differen tiation rules we are in a better position to pursue the applications of differentiation
in greater depth. Here we learn how derivatives affect the shape of a graph of a function and,
in particular, how they help us locate maximum and minimum values of functions. Many practical
problems require us to minimize a cost or maximize an area or somehow find the best possible
outcome of a situation. In particular, we will be able to investigate the optimal shape of a can and
to explain the location of rainbows in the sky.
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