# Tagged Questions

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### First derivative of Lagrange polynomial

Given the Lagrange basis polynomial as: $L_i(x)= \prod_{m=0, m \neq i}^n \frac{x-x_m}{x_i-x_m}$ is there a generic equation for the first derivative ${L_i}'(x)$ for any order,t hat is for any $n$?
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### total least squares derivation with matrices

Taken from a computer vision book: "to minimize the sum of the perpendicular distances between points and lines, we need to minimize $$\sum_i (ax_i + by_i +c)^2$$ subject to $a^2 +b^2 =1$. Now using ...
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### Lagrange multipliers from hell

I was asked to solve this question, decided to try and solve it with lagrange multipliers as I see no other way: "Find the closest and furthest points on the circle made from the intersection of the ...
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### Lagrange Method Problem

I am from engineering background and I am currently studying calculus. I had a question from assignment to be solved from a course on coursera but I could not do it. People have posted solution in the ...
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I have a function $y(x)$, that I would like to maximize, subject to two constraints. It is given by: $$\max_{x} \ y(x) = a \ cos(x) + b \ sin(x) \\ \text{subject to:} \\ x \geq 0 \\ x \leq ... 0answers 29 views ### How can I find the Min and max of this question? I have been trying for the past 2 hours on this question and cannot seem to figure out the answer. So far I have gotten the 'green' bits correct. Someone Help please 2answers 44 views ### How can I solve this using the Lagrange method? This is what I keep doing but the answer seems to be wrong every time. 1answer 289 views ### How to restrict Lagrange multiplier on positive values? Here's the function that i want to optimize:$$f(x,y) = x-2y$$and the constraint is:$$g(x,y) = x^2 + y - 10 = 0$$Solving with Lagrange multiplier I get:$$F(x,y) = x-2y - x^2\lambda - y\lambda ...
$x$ and $y$ are real numbers where satisfied the equation $x^2+y^2+xy-3x-3y-9=0$ Find the max. and min. values of $x^2+y^2$ I don't know how to find the constraint