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>
The value of f(-6) is -12.2
Explanation:
Given that the function 
We need to determine the value of f(-6)
The value of f(-6) can be determined by substituting the value for 
in the function and simplify the function.
Hence, let us substitute in the function, we get,
Let us apply the rule 
, we get,
Multiplying the numbers, we get,
The value of 
Substituting the value of , we get,
Subtracting the denominator, we have,
Dividing, we have,
Rounding off to the nearest tenth, we have,
Thus, the value of f(-6) is -12.2
Heyyyyyy new friends and I have no clue what the answer is cause I don’t feel like reading that but anyway yea nfs?
