Maximizing/Minimizing Points of z=-3x^2+54x+52y-3xy-2y^2+100

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How do you max/min points of the following equation

z=-3x^2+54x+52y-3xy-2y^2+100

regards

mb
 
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Find the points where dz/dx = dz/dy = 0. Use the second partial derivative test to check whether they are minima or maxima.
 
I would add that this isn't an implicit function. It's just two-variable. It's explicity defined
z=f(x,y) so finding the partials is pretty straight forward.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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