Question

How do you check the absolute max or min of a function along a line when unbounded with one critical point in 3 variables?

a) Use the Hessian matrix
b) Apply the Lagrange μltiplier method
c) Use the first derivative test
d) Set the second derivative equal to zero

Answer 1

To find the absolute max or min of a function along a line in three variables, use the Lagrange multiplier method while considering the line's constraints.

Step-by-step explanation:

To check the absolute maximum or minimum of a function along a line when unbounded with one critical point in three variables, one should typically use the Lagrange multiplier method. The first derivative test can help identify whether a critical point is a candidate for a local extremum but does not distinguish between a local and an absolute extremum. The Hessian matrix could provide information about the nature of a critical point, but it is not suitable by itself for finding extreme values along a line. Setting the second derivative equal to zero is not a conclusive method for finding absolute extrema, as it could represent points of inflection as well. To confidently find the absolute maximum or minimum, apply the Lagrange multiplier method while considering the constraints given by the line equation.