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I'm reading a book (Calculus Made Easy - Silvanus Thompson) that has the following exercise:
Divide a number N into two parts in such a way that three times the square of one part plus twice the square of the other part shall be a minimum.
It's part of a chapter that explains how to find minima/maxima using second-order derivatives. I'm quite confused on how to solve this problem.
I tried calculating the derivative of the following:
$$y = 3(xN)^2 + 2[(1-x)N]^2$$
Where $x$ represents a certain percentage of $N$. This gave me:
$$\frac{dy}{dx} = 2N(5x-2)$$
Which I then equated to $0$, which gave me the wrong value for $x$ when comparing to the answer key (which is $0.4N, 0.6N$). Clearly I'm doing it wrong.
Any help would be greatly appreciated. Please bear in mind that I'm trying to learn this stuff by myself without any proper math background.
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