Extrema
Task number: 3198
Find the global extrema for the following functions (also find the points that may be local extrema and try to determine whether at that point there really is a local extrema):
Variant 1
\(x^2 + (y-1)^2\)
Variant 2
\(x^2 - (y-1)^2\)
Variant 3
\(x^3 + (y-1)^3\)
Variant 4
\((x- y + 1)^2\)
Variant 5
\((x-y+1)^3\)
Variant 6
\(x^4 + y^4 - x^2 - y^2 - 2xy\)
Variant 7
\(xy + \frac{50}x + \frac{20}y\), \(x, y > 0\)
Variant 8
\((x^2 + y^2)e^{-(x^2 + y^2)}\)
Variant 9
\(\frac{ax + by + c}{\sqrt{x^2 + y^2 + 1}}\), \(a^2 + b^2 + c^2 \neq 0\)
Variant 10
\(\sin x + \sin y + \sin z - \sin(x+ y + z)\) pro \(x, y, z \in [0, \pi]\)
