A) If x^2+y^3−xy^2=19, find dy/dx in terms of x and y.

Question

dy/dx=________

B) Using your answer for dy/dx, fill in the following table of approximate y-values of points on the curve near x=1 y=3.

0.96 ______
0.98 ______
1.02 ______
1.04 ______

C) Finally, find the y-value for x=0.96 by substituting x=0.96 in the original equation and solving for y using a computer or calculator.
y(0.96)= ________

D) How large (in magnitude) is the difference between your estimate for y(0.96) using dy/dx and your solution with a computer or calculator?
___________

Answer 1

A)
x^2+y^3−xy^2=19
2x + 3y^2y' - y^2 - 2xyy' = 0
(3y^2-2xy)y' = y^2-2x

y' = (y^2-2x)/(3y^2-2xy)

B) Now just plug in the values
C) see wolframalpha.com
D) ...