<定理>若f'(a)＞0,則存在一正數d使得f(x)＜f(a) for all x in (a-d,a) 且f(a)＜f(x) for all x in (a,a+d)。
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f'''(a)＞0,則存在一正數d使得f''(x)＜f''(a) for all x in (a-d,a) 且f''(a)＜f''(x) for all x in (a,a+d)。
f''(x)＜0 for all x in (a-d,a) 且 0＜f''(x) for all x in (a,a+d)
f' decreases on (a-d,a) 且 f' incrases on (a,a+d)
f 凹向下 且 f 凹向上
故點(a,f(a))為inflection point
