Answer:
probability the student plays both instruments is [ ]
students who play both instruments = total students - flute players - piano players - students who play neither instruments
students who play both instruments
→ 31 - 4 - 14 - 7
→ 6 students play both instruments.
probability:
<h2>→Looks like .
The latter two critical points occur outside of since
so we ignore those points.
The Hessian matrix for this function is
The value of its determinant at (0, 0) is , which means a minimum occurs at the point, and we have
.
Now consider each boundary:
which has 3 extreme values over the interval of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).
and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).
which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).
which has 3 extreme values, but the previous cases already include them.
Hence has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).