PDA

View Full Version : Show that 3x^2-y^2+xy=4 is equal to y=2x when the gradient of the tangent is 8/3


natardy
Apr 14, 2011, 09:16 AM
Pure mathematics/module 1/implicit differntiation

galactus
Apr 14, 2011, 10:25 AM
Implicitly differentiate

3x^{2}-y^{2}+xy=4

to get y'.

Set the result = to 8/3 and solve for y.

dvmohanrao
May 31, 2011, 06:59 PM
3x^2-y^2+xy=4

differentiate implicitly

6x - 2y y ' + x y ' + y = 0

y ' (2y - x) = 6x + y

y ' = (6x + y)/(2y - x)

since gradient is 8/3

=> (6x + y)/(2y - x) = 8/3

=> 18x + 3y = 16y - 8x

=> 13y = 26x

=> y = 2x