Quiz 4
Quiz 4
Friday, April 6, 2001
NAME:
Student Number:_{}
No._{} Marks _{}
(20 Marks) Find the equation of the tangent line to the implicitly
defined function
4x^{3}y^{2}2x^{2}y^{3} = 40 at (2,1). 

Solution: Differentiating both sides of the given equation, we have
12x^{2}y^{2}+8x^{3}yy¢4xy^{3}6x^{2}y^{2}y¢ = 0. 

This implies
y¢ = 
4xy^{3}12x^{2}y^{2} 8x^{3}y6x^{2}y^{2}

. 

When x = 2 and y = 1, we obtain y¢ = 7/11. Hence, the equation of the
tangent line is
y = 
7 11

(x2)1 = 
7 11

x 
25 11

. 

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On 6 Apr 2001, 11:05.