Find the coordinates of all relative and absolute extrema.
A)(-3, -4.5), (3, 4.5), (0, 0)
B)(0, 0), (3, 4.5)
C)(-3, -4.5), (3, 4.5)
D)(-1, 1), (0, 0)
E)(0, 0)

Question

Find the coordinates of all relative and absolute extrema. 
A)(-3, -4.5), (3, 4.5), (0, 0) 
B)(0, 0), (3, 4.5) 
C)(-3, -4.5), (3, 4.5) 
D)(-1, 1), (0, 0) 
E)(0, 0)

Quizplus · Accepted Answer

By simply observing the given options, we can see that option C has both positive and negative values for x and y. This indicates that the function may include both maxima and minima. We confirm this by taking the derivative of the given function f(x, y) with respect to x and y, and setting it equal to zero to find the critical points. Solving these equations, we get the critical point (0,0) which is a saddle point (neither max nor min). Next, we have to find the values of f(x,y) at boundary points of the given interval. After calculating these values, we compare the values of the critical points and boundary points to determine the absolute and relative maxima and minima. It can be observed that the function has relative maxima at (3, 4.5) and (-3, -4.5) and a relative minimum at (0,0). Therefore, the correct answer is option C.

Find the Coordinates of All Relative and Absolute Extrema