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Unformatted text preview: on
x2 + 3
which f is increasing and those on which it is decreasing. Approximate all extrema.
Example 1.7.5. Let f (x) = Solution. Entering this function into the calculator gives Using the Minimum and Maximum features, we get 13
14 but does not prove
Although, truth be told, there is only one step of Calculus involved, followed by several pages of algebra. 76 Relations and Functions To two decimal places, f appears to have its only local minimum at (−1.73, −4.33) and its only
local maximum at (1, 73, 4.33). Given the symmetry about the origin suggested by the graph, the
relation between these points shouldn’t be too surprising. The function appears to be increasing on
[−1.73, 1.73] and decreasing on (−∞, −1.73] ∪ [1.73, ∞). This makes −4.33 the (absolute) minimum
and 4.33 the (absolute) maximum.
Example 1.7.6. Find the points on the graph of y = (x − 3)2 which are closest to the origin. Round
your answers to two decimal places.
Solution. Suppose a point (x, y ) is on the graph of y...
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