Explanation Given Information: The provided function is, g ( x ) = 2 x 3 − 6 x + 3 Calculation: Consider the provided function, g ( x ) = 2 x 3 − 6 x + 3 Differentiate both sides of the above equation with respect to x , g ′ ( x ) = 6 x 2 − 6 Locating stationary points: Stationary Points: Points in the interior of the domain where the derivative of the function is zero. To locate stationary points set g ′ ( x ) = 0 and solve for x . So, g ′ ( x ) = 0 6 x 2 − 6 = 0 Add 6 to both sides of the above equation: 6 x 2 − 6 + 6 = 6 6 x 2 = 6 Multiply both sides of the equation by 1 6 to get: 6 x 2 ⋅ 1 6 = 6 ⋅ 1 6 x 2 = 1 Take square root both sides of the above equation to get: x 2 = ± 1 x = ± 1 The domain of the function is [ − 2 , 2 ] , so x = ± 1 is in the interior of the domain. Thus, the only candidate for a stationary relative extremum occurs when x = ± 1 . Locating Singular points: Singular Points: Points in the interior of the domain where the derivative of the function is not defined. To locate singular points, find the interior points x where g ′ ( x ) is not defined but g ( x ) is defined. Since g ′ ( x ) is defined for all x in the interior of the domain, so there are no singular points. Locating end points: Since [ − 2 , 2 ] is the domain so the end points are x = − 2 and x = 2

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 12.1, Problem 16E

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To calculate: The exact location of the relative and absolute extrema of the function g(x)=2x3−6x+3 with domain [−2,2].

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Chapter 12.1, Problem 15E

Chapter 12.1, Problem 17E

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The exact location of the relative and absolute extrema of the function g ( x ) = 2 x 3 − 6 x + 3 with domain [ − 2 , 2 ] .

Solution Summary: The author calculates the exact location of relative and absolute extrema of the function g(x) with the domain

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To calculate: The exact location of the relative and absolute extrema of the function g(x)=2x3−6x+3 with domain [−2,2].

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Chapter 12 Solutions