(a) Give the partial derivatives of P. Pr,s)= 2rs +². - 5s + 2 Ps(r,s)= 2² +r2s - 5r (b) Which graph is steeper? OP(r,2) at r=3 P(3,s) at s=2 (c) Let C be a positive constant and let f(s)=P(C,s). Use your knowledge of quadratic functions to give a formula, in terms of C, for the value of s that gives the smallest value of f. S= cs² + s(c² - 5c) +2c|x
(a) Give the partial derivatives of P. Pr,s)= 2rs +². - 5s + 2 Ps(r,s)= 2² +r2s - 5r (b) Which graph is steeper? OP(r,2) at r=3 P(3,s) at s=2 (c) Let C be a positive constant and let f(s)=P(C,s). Use your knowledge of quadratic functions to give a formula, in terms of C, for the value of s that gives the smallest value of f. S= cs² + s(c² - 5c) +2c|x
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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![Consider the function P(r,s)=r²s+rs²-5rs+2r.
(a) Give the partial derivatives of P.
P/(r,s)= 2rs +². - 5s + 2
Ps(r,s) =
²
+r2s - 5r
(b) Which graph is steeper?
OP(r,2) at r=3
P(3,s) at s=2
(c) Let C be a positive constant and let f(s)=P(C,s). Use your knowledge of quadratic functions to give a formula, in
terms of C, for the value of s that gives the smallest value of f.
S=
cs² + s(c² - 5c) + 2c x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8747d92-b055-4562-9504-cd72cffb1b1f%2Fe0dce424-25c3-4432-8dfa-3b82a0ddc0e7%2F6newmn_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function P(r,s)=r²s+rs²-5rs+2r.
(a) Give the partial derivatives of P.
P/(r,s)= 2rs +². - 5s + 2
Ps(r,s) =
²
+r2s - 5r
(b) Which graph is steeper?
OP(r,2) at r=3
P(3,s) at s=2
(c) Let C be a positive constant and let f(s)=P(C,s). Use your knowledge of quadratic functions to give a formula, in
terms of C, for the value of s that gives the smallest value of f.
S=
cs² + s(c² - 5c) + 2c x
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