Problem Set B 1. The demand function for a good is given by the equation P = a - bQ while the total cost function is TC = dQ? + eQ + f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit. (b) Derive an expression for the value of Q for which profit is maximised. (2) For the f(x) = -x3 + 3x + 6 determine the coordinates of the turning point(s) and any point(s) of inflection, if they exist.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem Set B
1. The demand function for a good is given by the equation P = a – bQ while the total
cost function is TC = dQ² + eQ+ f, where a, b, d, e and f are positive constants.
(a) Derive the equation for profit.
(b) Derive an expression for the value of Q for which profit is maximised.
(2) For the f(x) = -x³ + 3x + 6 determine the coordinates of the turning point(s) and
any point(s) of inflection, if they exist.
(3) Using the appropriate approach covered in Unit 6 of this Course along with knowledge
gained in Unit 1 and 2, show that:
1
+
1
h
4
X - 1
x + 1
(a) Lim
(b) Lim
h→0 V5h + 4
= -2
X
· 2
t3
(c) Lim
t→1 t-1
1
= 3.
Transcribed Image Text:Problem Set B 1. The demand function for a good is given by the equation P = a – bQ while the total cost function is TC = dQ² + eQ+ f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit. (b) Derive an expression for the value of Q for which profit is maximised. (2) For the f(x) = -x³ + 3x + 6 determine the coordinates of the turning point(s) and any point(s) of inflection, if they exist. (3) Using the appropriate approach covered in Unit 6 of this Course along with knowledge gained in Unit 1 and 2, show that: 1 + 1 h 4 X - 1 x + 1 (a) Lim (b) Lim h→0 V5h + 4 = -2 X · 2 t3 (c) Lim t→1 t-1 1 = 3.
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