Finding the Gradient of a Difficult Curve: Tips and Hints

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In summary, the problem presents a curve with equation x^2 + xy + y^2 = 3 and asks for the gradient at the point (-1, k) in terms of k and the value of k when the tangent to the curve at this point is parallel to the x-axis. To solve this, implicit differentiation can be used to find the gradient dy/dx.
  • #1
don1231915
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Difficult gradient problem!

Consider the curve with equation x2 + xy + y2 = 3.
(a) Find in terms of k, the gradient of the curve at the point (−1, k).
(b) Given that the tangent to the curve is parallel to the x-axis at this point, find the
value of k.
 
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  • #2


don1231915 said:
Consider the curve with equation x2 + xy + y2 = 3.
(a) Find in terms of k, the gradient of the curve at the point (−1, k).
(b) Given that the tangent to the curve is parallel to the x-axis at this point, find the
value of k.

I hope you aren't done posting yet. You are going to show an attempt at solving it, right?
 
  • #3


Dick said:
I hope you aren't done posting yet. You are going to show an attempt at solving it, right?

yes, I have no idea how to do (a) but for b I tried substituting 1 and solve for y. I don't know if it is right
I am really confused when it asks for the slope

PLease help if you can!

Thank you so much

P.S. You don't have to provide me with a solution, just some hint or help would be more than helpful.
 
  • #4


don1231915 said:
yes, I have no idea how to do (a) but for b I tried substituting 1 and solve for y. I don't know if it is right
I am really confused when it asks for the slope

PLease help if you can!

Thank you so much

P.S. You don't have to provide me with a solution, just some hint or help would be more than helpful.

Ok, here's a hint. Try using implicit differentiation to find the gradient dy/dx. You know about that, yes?
 
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FAQ: Finding the Gradient of a Difficult Curve: Tips and Hints

What is a "Difficult gradient problem"?

A "Difficult gradient problem" refers to a challenging optimization problem where the goal is to find the maximum or minimum value of a function by adjusting its parameters. This can be a complex task when the function is high-dimensional and has many local optima.

What makes a gradient problem difficult?

A gradient problem can be difficult due to various reasons such as having a high-dimensional function, multiple local optima, and non-convexity. These factors make it challenging to find the global optimum and require advanced optimization techniques.

How is a difficult gradient problem solved?

A difficult gradient problem can be solved using various optimization techniques such as gradient descent, Newton's method, and simulated annealing. These methods use different approaches to find the optimal solution by iteratively adjusting the parameters of the function.

Can machine learning algorithms help with difficult gradient problems?

Yes, machine learning algorithms can be used to solve difficult gradient problems. Techniques such as neural networks, genetic algorithms, and reinforcement learning have been successful in finding optimal solutions for complex optimization problems.

What are the applications of solving difficult gradient problems?

Solving difficult gradient problems has various applications in fields like machine learning, data science, and engineering. It can be used to optimize parameters in neural networks, find the best fit for statistical models, and improve the efficiency of complex systems.

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