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Find the absolute h (x)= x'-3x²-9x-12 maximum and minimum values of the function the intenal on -2 Sx sl. Cleasly specify the value s. max and min

Find the absolute h (x)= x'-3x²-9x-12 maximum and minimum values of the function the intenal on -2 Sx sl. Cleasly specify the value s. max and min

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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**Problem Statement:** Find the absolute maximum and minimum values of the function \( h(x) = x^3 - 3x^2 - 9x - 12 \) on the interval \(-2 \leq x \leq 1\). Clearly specify the max and min values. **Explanation:** To solve this problem, one would typically follow these steps: 1. **Find the Critical Points:** Take the derivative of the function \( h(x) \), set it equal to zero, and solve for \( x \) to find critical points within the given interval. 2. **Evaluate the Function:** Calculate \( h(x) \) at each critical point and at the endpoints of the interval \(-2\) and \(1\). 3. **Compare Values:** Determine the maximum and minimum values from the set of function values obtained. This type of problem is commonly encountered in calculus while learning about maxima and minima, specifically in the context of applying derivatives to find extreme values on closed intervals.
Transcribed Image Text:**Problem Statement:** Find the absolute maximum and minimum values of the function \( h(x) = x^3 - 3x^2 - 9x - 12 \) on the interval \(-2 \leq x \leq 1\). Clearly specify the max and min values. **Explanation:** To solve this problem, one would typically follow these steps: 1. **Find the Critical Points:** Take the derivative of the function \( h(x) \), set it equal to zero, and solve for \( x \) to find critical points within the given interval. 2. **Evaluate the Function:** Calculate \( h(x) \) at each critical point and at the endpoints of the interval \(-2\) and \(1\). 3. **Compare Values:** Determine the maximum and minimum values from the set of function values obtained. This type of problem is commonly encountered in calculus while learning about maxima and minima, specifically in the context of applying derivatives to find extreme values on closed intervals.
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