Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function.
A) and ; relative maximum value: ; relative minimum value:
B) and ; saddle point: ; relative minimum value:
C) ; saddle point:
D) ; relative maximum value:
E) there are no critical points

Question

Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function. ​  ​
A) and ; relative maximum value: ; relative minimum value: 
B) and ; saddle point: ; relative minimum value: 
C) ; saddle point: 
D) ; relative maximum value: 
E) there are no critical points

Quizplus · Accepted Answer

The critical points are where the derivative is equal to zero or undefined. Setting the derivative of the given function equal to zero, we get 11eb651f_caea_8253_b0a1_69f5fee97a3b_TB8255_11, which gives two critical points, 11eb651f_caea_824e_b0a1_7d34ea4f10e4_TB8255_11 and 11eb651f_caea_824f_b0a1_9547bf655353_TB8255_11. The second derivative is 11eb651f_caea_8254_b0a1_4a2edaaf8ab8_TB8255_11. 
At 11eb651f_caea_824e_b0a1_7d34ea4f10e4_TB8255_11, the second derivative is positive, indicating a relative minimum.
At 11eb651f_caea_824f_b0a1_9547bf655353_TB8255_11, the second derivative is negative, indicating a relative maximum.
Therefore, the answer is (B).

Find the Critical Point(s) of the Function