has only one critical point at
. The function has Hessian
which is positive definite for all
, which means
attains a minimum at the critical point with a value of
.
To find the extrema (if any) along the boundary, parameterize it by
and
, with
. On the boundary, we have
Find the critical points along the boundary:
Respectively, plugging these values into
gives 11, 47, 43, and 47. We omit the first and third, as we can see the absolute extrema occur when
.
Now, solve for
for both cases:
so
has two absolute maxima at
with the same value of 47.
The answer is B. 7/48
Hope this helps!
A
substitute the given value for g into the expression and evaluate
- 5g - 6 = (- 5 × - 2 ) - 6 = 10 - 6 = 4 → A
