Apply of differentiation(2Q)!!

1. A circular cylinder of radius r cm is inscribed in a cone of base radius 6 cm and height 12cm. A smaller inverted right circular cone of a maximum volume is inscribe in the space inside the larger cone above the cylinder such that the apex of the smaller cone is at the centre of the upper base of the cylinder. Let V cm^3 be the total volume of the cylinder and the smaller cone.
Q: Find r such that V is a maximum.

2. let f(x) be a polynomial. If f(x)=(x-r)^2 g(x) where g(x) is unequal to 0, then r is a double roof of f(x)=0.
(a) If f(x)=0 has a double root r ,prove that f(r)=f'(r)=0
(b) Show that p(x)=(x-a)^n+(x+a)^n, where a is a non-zero real number, does not have a double real root.



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p.s 寫詳細步驟 Q1:ans: 324/77