Jerry asked in 科學數學 · 1 decade ago

critical number 的定義

If f is defined at c, then c is a critical number of f if f '(c)=0 or if f ' (c) is undefined

請問大大 undefined 請舉一個以上的例子說明一下是甚麼意思 ,我做題目好像做到 f '(x)undefined 時好像都沒有在其 f(x)的domain範圍中 所以都不是critical number 哪為什麼要這樣定義???

Update:

多一個問題 x=undefined 在那點是discontinue 那是怎樣的情況??

1 Answer

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  • Sen
    Lv 7
    1 decade ago
    Favorite Answer

    請參考這個網頁的五個例題 這裡我結路第五題作說明:

    http://www.analyzemath.com/calculus/applications/c...

    Example 5: Find the critical number(s) of function f defined by

    f(x) = (x - 2) 2/3 + 3

    Solution to Example 5.

    Note that the domain of f is the set of all real numbers. The derivative of f is

    f '(x) = (2/3)(x - 2) -1/3

    = 2 / [ 3(x - 2) 1/3]

    f ' is undefined at x = 2 and since x = 2 is in the domain of f it is a critical number.

    2009-12-17 19:07:50 補充:

    就像f(x) =1/x

    x 在 x=0 是未定義

    以y=1/x 的圖形看 x 可以是0.000000000000000000001

    但決不會等於0

    用圖形想 比較容易懂

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