Provide an appropriate response.Use the method of Lagrange multipliers to determine the critical points of f(x, y, z) = x2 + 4y - z2 subject to the constraint x + 2y - 4z = 3.
Fill in the blank(s) with the appropriate word(s).
(1, 9, 4)
Mathematics
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Solve the problem.Evaluate 
at (x, y, z) = (3, 2, 0) for the function u(p, q, r) = epq cos(r); p = 
, 
A. 12
B. 
C. 0
D. 24
Mathematics
The graph of a function f is provided. Determine the requested function value.f(2)
A. 3 B. -1 C. -3 D. 1
Mathematics
Solve the problem.A barge takes 6 hours to move (at a constant rate) downstream for 60 miles, helped by a current of 2 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip against the current.
A. 120 hours B. 10 hours C. 6 hours D. 8 hours
Mathematics
Find the number of terms in the arithmetic sequence.2, 
, 1, . . . , -6
A. 18 B. 16 C. 17 D. 15
Mathematics