MATH 151 University of Washington Find the Absolute Extrema Calculus Questions
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Application of Derivatives Homework
1) Find all absolute extrema for the following. If there are none, state why:
? ?
f=
( x ) tan x ? 2sec x on ?? ? , ??
? 4 4?
2) Find the absolute extrema for the following. If there are none, state why:
f (x) =
( x + 5) 3 x ? 4 on [ ?4,5]
2
3) Find the local extrema, inflection points, intervals where the function is increasing and
decreasing, and intervals of concavity. State intervals using interval notation:
( x + 1)
f (x) =
2
2
1+ x
4) A 10ft tall fence runs parallel to the side of a house 3 ft away. What is the length of the
shortest ladder that clears the fence and reaches the house?
5) A billboard 20 ft tall is located on top of a building with its lower edge 60 feet above the
level of the vieweràeye. How far from a point directly below the sign should a viewer
stand to maximize the angle ? between the lines of sight of the top and bottom of the
billboard? (This angle should result in the best view of the billboard) Hint-you may
want to use a trigonometric identities for sum/difference of angles.
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