Question

Can anyone help me with this calculus problem?
a) given the equation 4x^2 - 6xy + 4y^2 = 16, find dy/dx
b) what is the value at points (-2,2) and (1,-1)?
c) Interpret the meaning of these values

Answer 1

First thing to do would be to get the derivatives in respect to both x and y from left to right.
for example 2x^2-4xy its derivative would be 4xdx-4dxdy

Answer 2

so in this case the derivative would be 8x dx - 6 dx dy + 8 y dy = 0
0 since the derivative of any number is 0

understand me up to now? or do you have any questions?

Answer 3

i got the first part. what am i supposed to do for part b and c?

Answer 4

well for part B just plug in. To be honest, I'm kinda lost on A, glad you got the first part. Mind me telling me how you did it. But yea, for (-2,2) plug in -2 for your x and 2 for your y and then whatever you get is the value for that

Answer 5

for part A) dy/dx = 8x dy/dx - 6 x + 6y dy/dx + 8 y
-8x dy/dx - 6 y dy/dx = - 6x + 8y
dy/dx = (6x-8y)/(8x+6y)

Answer 6

thank you for helping me out

Answer 7

thanks, for the reminder, which I'll admit, I'm still a bit lost. But I'll get it in 5 or even 10 minutes tops ... I hope :o..

Answer 8

and no problem :)