SPs at (1, 0) (-1, 4) At (1, 0) Min At (-1, 4) Max Check points (0, 2) (2, 4) (-2, 0) Note that the turning points are and Local Max Local Min Max/Min applications Example Show that the rectangular area enclosed by 100 m of fencing is a maximum when it is a square. Let length be hence width = 50 x, x – Area A given by A is stationary for = 25 x Hence max for = 25 square. x –hence Increasing and decreasing functions Increasing functions: Decreasing functions: Example Show that is an increasing function for all x grad >0 Increasing function.
SPs at (1, 0) (-1, 4) At (1, 0) Min At (-1, 4) Max Check points (0, 2) (2, 4) (-2, 0) Note that the turning points are Local Max and Local Min Max/Min applications Example Show that the rectangular area enclosed by 100 m of fencing is a maximum when it is a square. Let length be x, hence width = 50 – x Area A given by A is stationary for x = 25 Hence max for x = 25 –hence square. Increasing and decreasing functions Increasing functions: Decreasing functions: Example Show that is an increasing function for all x grad >0 Increasing function.
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