Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 21: Problem 2

If \(z=f(x, y)=-11 x+y\) find (a) \(f(2,3)\) (b) \(f(11,1)\).

Short Answer

Expert verified
Question: Find the value of the function z = f(x, y) = -11x + y for the given points: (a) (2,3) and (b) (11,1). Answer: For the point (a), f(2,3) = -19, and for the point (b), f(11,1) = -120.

Step by step solution

01

(Step 1: Substitute the values of (a): x = 2, y = 3)

To find the value of z for the point (2,3), substitute x = 2 and y = 3 in the function definition. Do the following: \(z = f(x, y) = -11x+y\) \(z = -11(2) +3\)
02

(Step 2: Evaluate the expression for (a))

Now evaluate the expression for the point (2,3): \(z = -11(2) +3\) \(z = -22 + 3\) \(z = -19\) So, \(f(2,3) = -19\).
03

(Step 3: Substitute the values of (b): x = 11, y = 1)

Now, to find the value of z for the point (11,1), substitute x = 11 and y = 1 in the function definition. Do the following: \(z = f(x, y) = -11x+y\) \(z = -11(11) +1\)
04

(Step 4: Evaluate the expression for (b))

Now evaluate the expression for the point (11,1): \(z = -11(11) +1\) \(z = -121 + 1\) \(z = -120\) So, \(f(11,1) = -120\). To summarize, the values of the function z at the given points are: - for (a) \(f(2,3) = -19\) - for (b) \(f(11,1) = -120\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If \(p=\frac{R T}{V}\) where \(R\) is a constant, find \(\frac{\partial p}{\partial V}\) and \(\frac{\partial p}{\partial T}\)

If \(w=3 x y^{2}+2 y z^{2}\) find all first partial derivatives of \(w\) at the point with coordinates \((1,2,3)\)

Given \(z=f(x, y)=7 x+2 y\) find the output when \(x=8\) and \(y=2\).

Find all the second partial derivatives in each of the following cases: \(\begin{aligned}&\text { (a) } z=\ln x(\mathrm{~b}) z=\ln y & (\mathrm{c}) z=\ln x y\end{aligned}\) (d) \(z=x \ln y\) (e) \(z=y \ln x\)

Locate the position of any stationary points of the following functions: $$ f(x, y)=x^{2}+y^{3}-3 y $$
See all solutions

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Read Explanation

Fluids

Read Explanation

Waves Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Fields in Physics

Read Explanation

Atoms and Radioactivity

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free