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hnd the absolut max and min funcion fx,y)=(48x-lax²)cos L ón the rectangular Plate 1と×-3,-sys IT 4 Ht

hnd the absolut max and min funcion fx,y)=(48x-lax²)cos L ón the rectangular Plate 1と×-3,-sys IT 4 Ht

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Find the absolute max and min of the function \( f(x, y) = (48x - 12x^2) \cos y \) on the rectangular plate: \[ 1 \leq x \leq 3, \quad -\frac{\pi}{4} \leq y \leq \frac{\pi}{4} \]
Transcribed Image Text:Find the absolute max and min of the function \( f(x, y) = (48x - 12x^2) \cos y \) on the rectangular plate: \[ 1 \leq x \leq 3, \quad -\frac{\pi}{4} \leq y \leq \frac{\pi}{4} \]
Expert Solution
Step 1

Absolute maximum and minimum: - Assume that f(x) is defined on interval I. 
1. IfxM∈I and  f(x)≤f(xM) for every x∈I, we say that f(xM) is an absolute maximum on the interval I.
2. If xm∈I and f(xm)≤f(x) for every x∈I, we say that F(xm) is an absolute minimum on the interval I.

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