The three cases in the First Derivative Test cover the situations one commonly encounters but do not
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(a) Show that 0 is a critical number of all three functions but their derivatives change sign infinitely often on both sides of 0.
(b) Show that has neither a local maximum nor a local minimum at 0, has a local minimum, and has a local maximum.
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a fx x 4 sin 1x fx x 4 cos 1x 1x 2 sin 1x4x 3 4x 3 sin 1x x 2 cos 1x It is given that f0 0 so Since ...View the full answer
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