M2 differentiation

The slope of y = f(x) is positive means f '(x) > 0.
From graph,f '(x) > 0 is in the range 7 < x < 8.
Therefore,
(ai) : 7 < x < 8
When f '(x) = 0 and f ''(x) > 0 then it is a min;
when f '(x) = 0 and f ''(x) < 0 then if is a max;
when f '(x) = 0 and f ''(x) = 0 OR f ''(0) = 0 then it is a point of inflexion.
Therefore,
(aii) : x = 7 is the turning pt and it is a min
(aiii) : x = 2 is the point of inflextion
(aiv) : Sorry, I don't know how to plot graph on here. Anyway, the graph of y = f(x) like a 滑梯 upside down with x = 2 is flat and x = 7 is the min and then curve up.
(b) : This graph is a quadratic function like y = a(x - 2)*(x - 7) where 'a' is a positive number.
(ci) : This graph is the same as fig 2.3 with moving downwards 1 unit.
(cii) : No. As g(x) = f(x) - x, so f(x) - g(x) = x, which is postive only when x > 0, not for all x.

ai) 就咁睇圖，你想要步驟都冇~ x >7

aii ) 都係睇圖啦...因為f'(x)=0 先有turning point
所以，x=2 同x=7
之後問你 max or min

之後，最少值為例 左面應該係f'(x)<0 and 右面 f'(x) >0
先曲到最少值
但x=2 左右2方的值都係負數，所以只係stationary point

但x=7
左方係負數，右方係正數( 記住而家個圖係代表slope)

所以得出結論x=7係最少值

****如果你記得一條直線 ~曲左邊的slope係負數同曲右邊係正數，就會明我講咩

如果你只係識f''(x)黎試 最大or最才值 ，那我幫不了你









2011-12-24 22:29:27 補充：
步驟::講x=7+ 及7- 的slope大少係正or負
就証明到佢係最大or最少