Lagrange multipliers:







(if

)

(if

)

(if

)
In the first octant, we assume

, so we can ignore the caveats above. Now,

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of

.
We also need to check the boundary of the region, i.e. the intersection of

with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force

, so the point we found is the only extremum.
Answer:
C
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
dy/dx(1/4x + 14)=1/4
The answer is 16 pi - 16. The area of each triangle is 8, so both triangles are 16. The area of the circle is pi times the radius squared, 16 pi.