Find the extreme values of the function and where they occur.y = 
A. Absolute minimum value is 0 at x = 1. Absolute maximum value is 0 at x = -1.
B. Absolute minimum value is 0 at x = 0.
C. Absolute maximum value is 0 at x = 0.
D. Absolute minimum value is - 
at x = -1. Absolute maximum value is 
at x = 1.
Answer: D
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Find all the first order partial derivatives for the following function.f(x, y, z) = ln (xy)z
A. 
= - 
; 
= - 
; 
= ln (xy)
B. 
= 
; 
= 
; 
= ln (xy)
C. 
= 
; 
= 
; 
= z ln (xy)z-1
D. 
= z ln 
; 
= zln
; 
= ln (xy)
Indicate whether the statement is true always, sometimes, or never.A real number is a complex number.
A. Always B. Sometimes C. Never
Write the sum or difference as a product containing only sines and/or cosines.sin(6?) - sin(4?)
A. -2 sin ? cos(5?) B. 2 sin(5?) cos ? C. 2 sin ? cos(5?) D. -2 sin(5?) cos ?
Based on the graph, determine the range of f.f(x) = 
A. [0, 
]
B. [0, ?)
C. [0, 4]
D. [0, 4)