2xy
f(x, y) = 2x3 - 4y7 + xy p(x, y) =
x2+y2
2 z
g(x, y) = x sin ex +y2 r(x, y, z) = xy
h(x, y, z) = arctg (x + y + z) - 3(x2 + y2 + z2)3 d(x, y) = sin(x cos y)
f P
u
" "
2 2
f(x, y) = 3x3 - 4xy + 2 = , - P = (1, 4)
u
12 2
2 -2
f(x, y, z) = x + y2 + z3 = , , P = (-3, -2, -1)
u
3 3 3
f(x, y) = x2 = [0, 1] P = (10, 10)
u


1+y2
f(x, y) = f(x, y) = xy
sin x
"
" x 2y
f(x, y) = x - y f(x, y) = ee + ee
f(x, y, z) = (x + 1)(y + 2)(z + 3)
F
x2 cos x

F (x) = xy dy F (x) = x3y dy
x sin x


f(x, y) = (x - 3)2 + (y + 3)4 f(x, y) = 4y - y2 - x2
f(x, y) = x sin y f(x, y) = x4 + y3 + 32x - 9y
2 2
f fx fy
2 2
fx(x, y) = 6x + 4y fy(x, y) = 4x + 6y2 f(1, 1) = 9
2 2 x 1
fx(x, y) = 3x2 + cos(xy) fy(x, y) = -4y + cos(xy) - sin(xy) f(0, 1) = 0
y y2
2 2 1
fx(x, y) = 2x3 + ln y fy(x, y) = f(1, 1) = 2
xy

f(x, y) = xy + y2 + x - y f(x, y) = x2 - 2y2
xy
f(x, y) = f(x, y) = yx2 + y3 - 4x2
x2+y2+1
f(x, y) = ex sin y f(x, y) = x2 - 6x cos y + 9
f U ‚" R2

f(x, y) = x2 + 2xy + 3y2 U = {(x, y) : -2 x 4, -1 y 3}
f(x, y) = x2 - 4xy + y3 + 4y U (-1, -1) (7, -1) (7, 7)
f(x, y) = x2 - 2y2 U = {(x, y) : x2 + y2 4}
f(x, y) = 4x3 - 2x2y + y2 U
y = x2 y = 9
f(x, y) = xy3
(0, 0, 0)
4x - 3y + z = 5
P = (2, 1, -1)