The function 𝑓(𝑥,𝑦)=𝑥3−3𝑥−2𝑥𝑦−𝑦2−2𝑦+4 has two critical points. Find and classify them

The function 𝑓(𝑥,𝑦)=𝑥3−3𝑥−2𝑥𝑦−𝑦2−2𝑦+4 has two critical points. Find and classify them

Show that the following system of equations has unique solutions. Find its solution by thereduction method𝑥 + 𝑦 + 𝑧 = 2, 𝑥 − 2𝑦 + 𝑧 = 8, 3𝑥 + 𝑦 + 𝑧 = 4

If 𝑧=𝑠𝑖𝑛⁡(3𝑥+2𝑦), determine 3∂2𝑧∂𝑦2-2∂2𝑧∂𝑥2Question 9Answera.-6𝑠𝑖𝑛⁡(3𝑥+2𝑦)b.12𝑠𝑖𝑛⁡(3𝑥+2𝑦)c.6𝑧d.6𝑐𝑜𝑠⁡(3𝑥+2𝑦)

If 𝑢 = 𝑥2 tan−1 𝑦𝑥 − 𝑦2 tan−1 𝑥𝑦 show that 𝜕2𝑢𝜕𝑥𝜕𝑦 = 𝑥2−𝑦2𝑥2+𝑦2 and 𝜕2𝑢𝜕𝑥𝜕𝑦 = 𝜕2𝑢𝜕𝑦𝜕𝑥.

Is the sentence ∃𝑦∀𝑥𝑆(𝑥,𝑦)∃𝑦∀𝑥𝑆(𝑥,𝑦) true under the interpretation where 𝑥𝑥 and 𝑦𝑦 range over the integers and 𝑆(𝑥,𝑦)𝑆(𝑥,𝑦) is "𝑦<(𝑥+2)2𝑦<(𝑥+2)2"?