The table shows the favourite colour of 400 people. Complete the table and draw a pie chart to represent this information? Maths
1 answer:
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a.
Critical points occur where . The exponential factor is always positive, so we have
b. As the previous answer established, the critical point occurs at (-3, 8) if and
.
c. Check the determinant of the Hessian matrix of :
The second-order derivatives are
so that the determinant of the Hessian is
The sign of the determinant is unchanged by the exponential term so we can ignore it. For and
, the remaining factor in the determinant has a value of 4, which is positive. At this point we also have
which is negative, and this indicates that (-3, 8) is a local maximum.