1. a) Copy and complete the table below: Original Function First derivative Second Derivative Original Function First derivative Second Derivative 5 f(t)=-3- t - 5e 0 a) Find the profit function. b) After completing the table in part 1 a) above, copy and complete the table below by stating the name of EACH function used and their respective derivatives: f(z) = ln100 2. a) Differentiate the function Q(P) = -2₁√/p³(e²-√P b) Hence or otherwise, determine Q'(1). h(p) = -2e¹-p 3. A R&C Ltd produces and sells 6" Cider Blocks. R&C Ltd has a revenue function of R(q) = 2q² +50q+600 and a cost function of C(q) = 3q² + 100, where R and C are measured in thousands of dollars and q represent the number of Cider Blocks in thousands of dollars that are produced and sold.
1. a) Copy and complete the table below: Original Function First derivative Second Derivative Original Function First derivative Second Derivative 5 f(t)=-3- t - 5e 0 a) Find the profit function. b) After completing the table in part 1 a) above, copy and complete the table below by stating the name of EACH function used and their respective derivatives: f(z) = ln100 2. a) Differentiate the function Q(P) = -2₁√/p³(e²-√P b) Hence or otherwise, determine Q'(1). h(p) = -2e¹-p 3. A R&C Ltd produces and sells 6" Cider Blocks. R&C Ltd has a revenue function of R(q) = 2q² +50q+600 and a cost function of C(q) = 3q² + 100, where R and C are measured in thousands of dollars and q represent the number of Cider Blocks in thousands of dollars that are produced and sold.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer all questions.
Transcribed Image Text:1.
a) Copy and complete the table below:
Original Function
First derivative
Second Derivative
5
f(t) = -3-5e
t
Original Function
First derivative
Second Derivative
0
b) After completing the table in part 1 a) above, copy and complete the
table below by stating the name of EACH function used and their
respective derivatives:
f(z) = ln100
2. a) Differentiate the function Q(P) = -2₁√/p³(e²-√³)
b) Hence or otherwise, determine Q'(1).
a) Find the profit function.
h(p) = -2e¹-p
3. A R&C Ltd produces and sells 6" Cider Blocks. R&C Ltd has a revenue
function of R(q) = 2q² +50q+600 and a cost function of C(q) = 3q² +
100, where R and C are measured in thousands of dollars and q represent the
number of Cider Blocks in thousands of dollars that are produced and sold.
b) Determine the number of Cider Blocks needed to maximize R&C Ltd's profit.
c) In your view, is R&C Ltd's rate of profit increasing or decreasing when 30,000
6" Cider Blocks are produced and sold? Give reasons for your
answer.
d) Calculate R&C Ltd's maximum profit.
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