Explanation Given Information: The provided function is, f ( x , y ) = 10 , 000 + 5 x − 4 y Formula Used: The partial derivatives of f with respect to x is the derivative of f with respect to x , when all other variables are treated as constant and is denoted as ∂ f ∂ x . The derivative formula, d d x ( x n ) = n x n − 1 And, d d x ( constant ) = 0 Where, n is any real number. Calculation: Consider the provided function, f ( x , y ) = 10 , 000 + 5 x − 4 y To calculate the value of ∂ f ∂ x , treat − 4 y as a constant. Thus, ∂ f ∂ x = ∂ ∂ x ( 10 , 000 + 5 x − 4 y ) = ∂ ∂ x ( 10 , 000 ) + ∂ ∂ x ( 5 x ) − ∂ ∂ x ( 4 y ) = 0 + 5 + 0 = 5 And, for the value of ∂ f ∂ x | ( 1 , − 1 ) , substitute 1 for x and − 1 for y in the value obtained for ∂ f ∂ x , ∂ f ∂ x | ( 1 , − 1 ) = 5 Now, to calculate the value of ∂ f ∂ y , treat 5 x as a constant

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

7th Edition

ISBN: 9781337291293

Author: Waner, Stefan; Costenoble, Steven

Publisher: Brooks Cole

See similar textbooks

Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Videos

Question

Chapter 8.2, Problem 2E

To determine

To calculate: The values of ∂f∂x, ∂f∂y, ∂f∂x|(1,−1)and ∂f∂y|(1,−1) where f(x,y)=10,000+5x−4y.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 1E

Chapter 8.2, Problem 3E

Students have asked these similar questions

A graph of the function f is given below: Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1 Of is defined at a. If is not defined at x = a. Of is continuous at x = a. If is discontinuous at x = a. Of is smooth at x = a. Of is not smooth at = a. If has a horizontal tangent line at = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. If has no tangent line at x = a. f(a + h) - f(a) lim is finite. h→0 h f(a + h) - f(a) lim h->0+ and lim h h->0- f(a + h) - f(a) h are infinite. lim does not exist. h→0 f(a+h) - f(a) h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

The graph below is the function f(z) 4 3 -2 -1 -1 1 2 3 -3 Consider the function f whose graph is given above. (A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter "DNE". If a limit can be represented by -∞o or ∞o, then do so. lim f(z) +3 lim f(z) 1-1 lim f(z) f(1) = 2 = -4 = undefined lim f(z) 1 2-1 lim f(z): 2-1+ lim f(x) 2+1 -00 = -2 = DNE f(-1) = -2 lim f(z) = -2 1-4 lim f(z) 2-4° 00 f'(0) f'(2) = = (B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left- continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If there are none, enter "none". Discontinuous at z = Left-continuous at x = Invalid use of a comma.syntax incomplete. Right-continuous at z = Invalid use of a comma.syntax incomplete. (C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5).…

A graph of the function f is given below: Study the graph of f at the value given below. Select each of the following that applies for the value a = -4. f is defined at = a. f is not defined at 2 = a. If is continuous at x = a. Of is discontinuous at x = a. Of is smooth at x = a. f is not smooth at x = a. If has a horizontal tangent line at x = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. Of has no tangent line at x = a. f(a + h) − f(a) h lim is finite. h→0 f(a + h) - f(a) lim is infinite. h→0 h f(a + h) - f(a) lim does not exist. h→0 h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

Chapter 8 Solutions

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 6E Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The values of ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ x | ( 1 , − 1 ) and ∂ f ∂ y | ( 1 , − 1 ) where f ( x , y ) = 10 , 000 + 5 x − 4 y .

Concept explainers

Videos

To calculate: The values of ∂f∂x, ∂f∂y, ∂f∂x|(1,−1)and ∂f∂y|(1,−1) where f(x,y)=10,000+5x−4y.

Want to see the full answer?

Chapter 8 Solutions