Explanation Given: The provided function is: f ( x ) = 5 − x 2 / 3 . Formula used: Write the formula for derivative of power rule. If f ( x ) = x n for any number n , then the derivative. f ′ ( x ) = n x n − 1 If f ( x ) = k for any real number k , then the derivative is defined by the formula. f ′ ( x ) = 0 To find local maximum and minimum find the values of x from the equation f ′ ( x ) = 0 . Then find f ″ ( x ) and put the values of x. If f ″ ( x ) equals some positive quantity then it will be Local minimum is located at that point x and if f ″ ( x ) equals some negative quantity then Local maximum is located at the point at that point. Calculation: Consider the provided equation: f ( x ) = 5 − x 2 / 3 …… (1) Differentiate the function with respect to x by using the power rule of the derivative. f ′ ( x ) = 0 − 2 3 x − 1 / 3 = − 2 3 x − 1 / 3 …… (2) Calculate the critical point by equating it to zero. Substitute 0 for f ′ ( x ) . 0 = − 2 3 x − 1 / 3 Solve for x

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ISBN: 9780134773285

Author: MULLINS

Publisher: YUZU

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Chapter 12.1, Problem 29E

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To calculate: The location of local extremum of the function f(x)=5−x2/3.

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Chapter 12.1, Problem 28E

Chapter 12.1, Problem 30E

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Chapter 12 Solutions

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The location of local extremum of the function f ( x ) = 5 − x 2 / 3 .

Solution Summary: The author explains how to calculate the location of local extremum of the function f(x)=5-x

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To calculate: The location of local extremum of the function f(x)=5−x2/3.

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