Define (x) x 3 sin(1 x) for x 0 and (0) 0 (a) Show that ' is continuous at x 0 and that x 0 is a critical point of (b) Examine the graphs of and ' Can the First Derivative Test be applied (c) Show that (0) is neither a local min nor a local max

Question: Define (x) = x 3 sin(1/x) for x 0 and (0) = 0. (a) Show that ' is continuous at x = 0 and

Define ƒ(x) = x³sin(1/x) for x ≠ 0 and ƒ(0) = 0.
(a) Show that ƒ' is continuous at x = 0 and that x = 0 is a critical point of ƒ.
(b) Examine the graphs of ƒ and ƒ'. Can the First Derivative Test be applied?
(c) Show that ƒ(0) is neither a local min nor a local max.

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