fxx, fxy, fyx, and fyy
f(x, y) = y (ln x)
fxx, fxy, fyx, and fyy
f(x, y) = y (ln x)
Suppose that the function f(x, y) has continuous partial
derivatives fxx, fyy, and fxy at all...
Suppose that the function f(x, y) has continuous partial
derivatives fxx, fyy, and fxy at all points (x,y) near a critical
points (a, b). Let D(x,y) = fxx(x, y)fyy(x,y) – (fxy(x,y))2 and
suppose that D(a,b) > 0.
(a) Show that fxx(a,b) < 0 if and only if fyy(a,b) <
0.
(b) Show that fxx(a,b) > 0 if and only if fyy(a,b) >
0.
Find fxx(x,y), fxy(x,y),
fyx(x,y), and fyy(x,y) for the function f
f(x,y)= 8xe3xy
Find fxx(x,y), fxy(x,y),
fyx(x,y), and fyy(x,y) for the function f
f(x,y)= 8xe3xy
Find fxx, fxy, fyy when f(x, y) = xe^(x^2−xy+y^2)
Find fxx, fxy, fyy when f(x, y) = xe^(x^2−xy+y^2)
. For the function x,y=xarctan(xy) , compute
fx , fy ,
fxx , fyy , and...
. For the function x,y=xarctan(xy) , compute
fx , fy ,
fxx , fyy , and
fxy
Consider the function f(x,y) = xe^((x^2)-(y^2))
(a) Find f(1,−1), fx(1,−1), fy(1,−1). Use these values to find...
Consider the function f(x,y) = xe^((x^2)-(y^2))
(a) Find f(1,−1), fx(1,−1), fy(1,−1). Use these values to find a
linear approximation for f (1.1, −0.9).
(b) Find fxx(1, −1), fxy(1, −1), fyy(1, −1). Use these values to
find a quadratic approximation for f(1.1,−0.9).
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the...
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...