Question

英文微积分题目

Area A right triangle is formed in the first quadrant by the X- and y-axes and a line through the point (2,3). Find the vertices of the triangle so that its area is miniumu.
Volume Find the volume of the largest right circular cone that can be inscribed in a sphere of radius r. (= =图是一个球里面有个圆锥，圆锥和球体是接触的)

Answer 1

The method to solve optimization question is :

1、Equate；

2、Find the stationary point;

3、Find the second derivative

      A、if second derivative is positive, 

           the curve concaves up,

           the staionary point is minimum point (minima).

      B、if second derivative is negative, 

           the curve concaves down,

           the staionary point is maximum point (maxima).

The detailed solution below is for your reference.