(a) For matrix A = ( ), ifg(X) = X? + 4x+2, what is the answer to g(A)? (b) Using algebra, find the solution to the system of inequalities below ys 5- 3x y + 192 x? – 8x (c) What is peculiar about the slope of a function before and after a point of inflection as compared with the slope before or after a maximum or minimum point?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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(a) Find the following:
i. Lim →
x/ + 9x/ 6x/ − 4x/
ii. Lim →
(2x − 1)/ − 3 x − 5


(b) The total revenue curve of a firm is R(q) = 40q − 12q and its
average cost A(q) =
1 30
q − 12.85q + 20 +
400 q
,where q is the firms output.
i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?

(a) For matrix A = ( ), ifg(X) = X? + 4x+2, what is the answer to g(A)?
(b) Using algebra, find the solution to the system of inequalities below
ys 5- 3x
y + 192 x? – 8x
(c) What is peculiar about the slope of a function before and after a point of inflection
as compared with the slope before or after a maximum or minimum point?
Transcribed Image Text:(a) For matrix A = ( ), ifg(X) = X? + 4x+2, what is the answer to g(A)? (b) Using algebra, find the solution to the system of inequalities below ys 5- 3x y + 192 x? – 8x (c) What is peculiar about the slope of a function before and after a point of inflection as compared with the slope before or after a maximum or minimum point?
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