Answered: Determine the absolute minimum and…

Determine the absolute minimum and maximum values on the given interval for each function below. (a) x)4rr2-24r+15 on [-2,3] (b) gx) 4 on1,5]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 60RE

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Question

Determine the absolute minimum and maximum values on the given interval for each function below.
(a) x)4rr2-24r+15 on [-2,3]
(b) gx) 4 on1,5]

Expert Solution

Step 1

(a)

Consider the function f(x) = 4x³ -6x² -24x +15 on [-2, 3].

Obtain the first derivative of the function as follows.

Calculus homework question answer, Step 1, Image 1

Step 2

Substitute x = 2, –1, –2 and 3 in f (x) for obtain the maximum and minimum values.

Construct a table for f (x) corresponding x value as given below.

Calculus homework question answer, Step 2, Image 1

Step 3

(b)

Consider the function g(x) = (x² - 4 )^2/3 on [-1, 5].

Obtain the first derivative of the function as follows.

Calculus homework question answer, Step 3, Image 1

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