Let f(x, y, z) = xyz. Find the point(s) where f(x, y, z) may have a possible relative maximum or minimum, subject to the constraint x + 6y + 3z = 36 and where x > 0, y > 0, z > 0. Use the method of Lagrange multipliers.Enter your answer as just (a, b, c) where a, b, c are all integers.
Fill in the blank(s) with the appropriate word(s).
(12, 2, 4)
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Provide an appropriate response.It can be shown that 
= 0 for c > 0. Find the smallest value of N such that 
for all 
if 
and 
A. 31 B. 28 C. 35 D. 25
Solve the problem.Tina Thompson scored 32 points in a recent basketball game without making any 3-point shots. She scored 22 times, making several free throws worth 1 point each and several field goals worth two points each. How many free throws did she make? How many 2-point field goals did she make?
A. 14 free throws, 9 field goals B. 12 free throws, 10 field goals C. 10 free throws, 12 field goals D. 13 free throws, 9 field goals
Graph the quadratic function using its vertex, axis of symmetry, and intercepts.f(x) = x2 - 6x
A. vertex (3, 9)
intercept (0, 18)
B. vertex (3, -9)
intercepts (0, 0), (6, 0)
C. vertex (-3, -9)
intercepts (0, 0), (-6, 0)
D. vertex (-3, 9)
intercept (0, 18)
Solve.5x + 10 - 4x = 3 - 4
A. -9 B. 9 C. 11 D. -11