Josephood7

Find the critical point of the function [math].

[math] 
Use the Second Derivative Test to determine whether it is
 A. a saddle point
 B. a local minimum
 C. a local maximum
 D. test fails

Note: You can earn partial credit on this problem.

The figure shows the level curves of a function [math] around a maximum or a minimum [math]. One of the points P or Q has coordinates [math] and the other has coordinates [math]. Suppose [math] and [math]. Consider the two linear approximations to [math] given by [math] (a) What is the relationship between the values of [math] and [math]?  A. [math]  B. [math]  C. [math]  D. [math] (b) What are the coordinates of point P?  A. [math]  B. [math] (c) Is M a maximum or a minimum?   ?    Maximum    Minimum    (d) Is the sign of [math] positive or negative?   ?    Positive    Negative    (e) Is the sign of [math] positive or negative?   ?    Positive    Negative

(Click on graph to enlarge)

Note: You can earn 60% partial credit for 3 - 4 correct answers.

Find the parabola of the form [math] which best fits the points [math], [math], [math] by minimizing the sum of squares, [math], given by [math]

[math]