Identify a f(x) function that has these characteristics:
f(–5) = f(2) = 0; f '(-1.5) = 0, f '(x) < 0 for x < -1.5; f '(x) > 0 for x > -1.5
please help!
Math question need help?
2015-09-17 3:06 am
回答 (1)
2015-09-17 10:12 am
✔ 最佳答案
f(–5) = f(2) = 0So we may assume that f(x) = a(x+5)(x-2)
f(x) = a(x+5)(x-2) = a ( x^2 + 3x - 10 )
f ' (x) = a(2x+3)
f ' (-1.5) = a(-3+3) = 0
When x > - 1.5 ,
then 2x+3 > 0
so f ' (x) = a(2x+3) > 0 implies a > 0
When x < - 1.5 ,
then 2x+3 < 0
so f ' (x) = a(2x+3) < 0 implies a > 0
Ans: f(x) = a ( x^2 + 3x - 10 ) , for any a > 0
收錄日期: 2021-05-02 14:08:42
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