For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
Answer:
Step-by-step explanation:
Consider the given differential equation is
Taking all variables on right sides.
Let as assume,
and 
Find partial derivatives 
and 
and 
Since 
, therefore the given differential equation is exact.
The solution of the exact differential equation is
Answer:
D
Step-by-step explanation:
Answer:
Reggies makes sence
Step-by-step explanation:
It’s similar to D because they are going to have the same measured angle
