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


4x3y2-2x2y3 = 40   at (2,-1).

Solution: Differentiating both sides of the given equation, we have


12x2y2+8x3yy-4xy3-6x2y2y = 0.

This implies


y = 4xy3-12x2y2
8x3y-6x2y2
.

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


y = 7
11
(x-2)-1 = 7
11
x- 25
11
.



File translated from TEX by TTH, version 2.79.
On 6 Apr 2001, 11:05.