Implicit Differentiation [SOLVED]

In summary, The problem involves solving for the value of m at the point (3,-4) where the equation -4x^2+3xy+4y^3=-328 is given. The solution involves using implicit differentiation and plugging in the values to get an answer of m=-12/67. However, there was some confusion about the sign of the answer, but it was eventually corrected.
  • #1
hard_assteel
12
0
[SOLVED] Implicit Differentiation

-4x^2+3xy+4y^3=-328

This is at the point (3,-4)
and i am trying to find m


Homework Equations





The Attempt at a Solution



here is my work

-4x^2+3xy+4y^3=-328
-8x+3xy'+3y+12y^2y'=0
-8x+3y=-3xy'-12y^2y'
-8x+3y=[-3x-12y^2]y'
y'=(-8x+3y)/(-3x-12y^2)
plug in x=1,y=3 then solve and get
m=-12/67
can you find the error?
It would be very much appreciated
thank you.
 
Last edited:
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  • #2
Try plugging in the values to your final expression again.
 
  • #3
0h, the answer is correct, it just needs to be not negative, thank you. i was about to go crazy
 
Last edited:
  • #4
hard_assteel said:
0h, the answer is correct, it just needs to be negative, thank you. i was about to go crazy

I don't agree that your numerical answer is correct, regardless of the sign.
 
  • #5
yeah, its correct i just checked. thankx for helping me:smile:
 
  • #6
hard_assteel said:
yeah, its correct i just checked. thankx for helping me:smile:

Well, maybe it is now you've changed the point to (3,-4)!
 

What is implicit differentiation?

Implicit differentiation is a mathematical method used to find the derivative of a function that is not written explicitly in terms of the independent variable. It is commonly used when the dependent variable cannot be easily solved for in terms of the independent variable.

How is implicit differentiation different from explicit differentiation?

Explicit differentiation involves finding the derivative of a function that is written explicitly in terms of the independent variable. Implicit differentiation, on the other hand, involves finding the derivative of a function that is not written explicitly in terms of the independent variable.

When should implicit differentiation be used?

Implicit differentiation should be used when it is difficult or impossible to solve for the dependent variable in terms of the independent variable. This often occurs when the function is too complex to be solved algebraically.

What is the process of implicit differentiation?

The process of implicit differentiation involves treating the dependent variable as a function of the independent variable, taking the derivative of both sides of the equation with respect to the independent variable, and then solving for the derivative of the dependent variable. This may involve using the chain rule or product rule.

What are some real-world applications of implicit differentiation?

Implicit differentiation is commonly used in physics and engineering to find rates of change and slopes of curves that cannot be easily solved for explicitly. It is also used in economics to analyze production functions and in biology to model population growth.

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