MHB Implicit differentiation question

Click For Summary
The discussion revolves around finding the derivative of the equation 2xy^8 + 7xy = 27 at the point (3,1) using implicit differentiation. Participants clarify that the initial confusion stems from not clearly stating the problem, which should confirm that (3,1) satisfies the equation. The implicit differentiation yields the derivative as y' = -3/23 after substituting the point into the differentiated equation. This result addresses the original request for help with implicit differentiation. The thread emphasizes the importance of clear problem statements in mathematical discussions.
rcurrie
Messages
1
Reaction score
0
Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
 
Physics news on Phys.org
rcurrie said:
Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
Can you post the different answers with the respected work?

Thanks
Cbarker1
 
rcurrie said:
Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
Answers to what question? There is no question or problem here!

IF the problem is "show that (3,1) satifies 2xy^8+ 7xy= 27" or "show that (3, 1) lies on the graph of 2xy^8+ 7xy= 27" then it is basic integer arithmetic.

2(3)(1)^8= 2(3)= 6.
7(3)(1)= 7(3)= 21.

What is the sum of 6 and 21?
 
rcurrie said:
Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
The thread title mentions implicit differentiation. So, differentiate implicitly: $$2y^8 + 16xy^7y' + 7y + 7xy' = 0.$$ At the point $(3,1)$ that becomes $2 + 48y' + 7 + 21y' = 0$. so $69y' + 9 = 0$. That gives $y' = -\dfrac3{23}$. Is that the answer you are looking for?
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
View full post »

Similar threads

Undergrad Questions about implicit differentiation?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Can Implicit Differentiation Be Done by Separation of Variables?
  • · Replies 2 ·
Replies
2
Views
1K
High School Implicit differentiation or just explicit?
  • · Replies 2 ·
Replies
2
Views
1K
Digging deeper into (implicit) differentiation and integration
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Why Do Implicit Differentiation Results Differ When Multiplying by x or y?
  • · Replies 4 ·
Replies
4
Views
2K
Implicit Differentiation: Differentiating in Terms of X
  • · Replies 7 ·
Replies
7
Views
2K
MHB Implicit Differentiation to find equation of a tangent line
  • · Replies 4 ·
Replies
4
Views
2K
How is implicit differentiation performed in calculus?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad How to evaluate the enclosed area of this implicit curve?
  • · Replies 2 ·
Replies
2
Views
3K
Implicit Differentiation Question - Stuck
  • · Replies 3 ·
Replies
3
Views
1K