Consider the function f(x, y) = 4xy − 2x 4 − y
2 .
(a) Find the critical points of f.
(b) Use the second partials test to classify the critical
points.
(c) Show that f does not have a global minimum.
The function f(x, y) = 10−x 2−4y 2+2x has one critical point.
Find that critical point and show that it is not a saddle point.
Indicate whether this critical point is a maximum or a minimum, and
find that maximum or minimum value.
A) Solve the initial value problem:
8x−4y√(x^2+1) * dy/dx=0
y(0)=−8
y(x)=
B) Find the function y=y(x) (for x>0 ) which
satisfies the separable differential equation
dy/dx=(10+16x)/xy^2 ; x>0
with the initial condition y(1)=2
y=
C) Find the solution to the differential equation
dy/dt=0.2(y−150)
if y=30 when t=0
y=