Mathematics M coursework~~ 帮忙~~~~

perhapslove

The cubic function is one of the most frequency occurring functions. It is interesting to investigate some properties of a cubic function.

1. Consider a cubic function f(x):ax^3+b , where a and b are real number and a not equal to 0. The shape of the graph of the cubic function depends on the value on the values of a and b.

（a） Investigate the shape of the graph of the cubic function for various value of a for the case b=0. Identify the point of inflexion.

（b） Investigate the shape of the graph if both a and b have the same sign and if a and b have different signs. Identify the point of inflexion in each case.

（c) Investigate the points of intersection of the graphs of f and its tangents. What can u say abt the number of point of intersection.

姷婈蝶湘

0.0 我已經回复你了 不知你看到沒 我在這重貼吧 ;D

perhapslove 发表于 31-8-2012 02:39 AM
The cubic function is one of the most frequency occurring functions. It is interesting to investig ...

1. Consider a cubic function f(x):ax^3+b , where a and b are real number and a not equal to 0. The shape of the graph of the cubic function depends on the value on the values of a and b.

（a） Investigate the shape of the graph of the cubic function for various value of a for the case b=0. Identify the point of inflexion.
做6個graph, 分別3個-a, 3個+a, 最好就是號碼相差很大, 可以看得出graph的形狀的變化 eg, -20, -5, -1/2, +1/2, +5, +20
（b） Investigate the shape of the graph if both a and b have the same sign and if a and b have different signs. Identify the point of inflexion in each case.
做4個graph 分別 +a+b, +a-b, -a+b, -a-b , a和b的號碼自己喜歡
（c) Investigate the points of intersection of the graphs of f and its tangents. What can u say abt the number of point of intersection.
做大概6個graph, 用回(1a)的equation 做也行, 使用differentiation 找出你用的equation的tangent的equation, 把graph畫上, 就會看到有points of intersection, 有些有2個, 有些有1個