Explanation Given: The function is: g ( x ) = 3 x − 4 x 3 / 4 . 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 implies Local minimum is located at point x and if f ″ ( x ) equals some negative quantity then Local maximum is located at that point. Calculation: Consider the given function: g ( x ) = 3 x − 4 x 3 / 4 …… (1) Differentiate g ( x ) with respect to x . d d x ( g ( x ) ) = d d x ( 3 x − 4 x 3 / 4 ) g ′ ( x ) = d d x ( 3 x ) − d d x ( 4 x 3 / 4 ) g ′ ( x ) = 3 − 3 4 ( 4 ) x ( ( 3 / 4 ) − 1 ) Solve further, g ′ ( x ) = 3 − 3 x − 1 / 4 …… (2) Now, find the values of x for which g ′ ( x ) becomes zero. Therefore, 3 − 3 x − 1 / 4 = 0 − 3 x − 1 / 4 = − 3 x − 1 / 4 = 1 x = ( 1 ) 1 / 4 Solve for x

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Chapter 12.3, Problem 21E

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To calculate: The locations of absolute extrema of the function given below on the given interval:

g(x)=3x−4x3/4 ;(0,∞)

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Chapter 12.3, Problem 20E

Chapter 12.3, Problem 22E

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Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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The locations of absolute extrema of the function given below on the given interval: g ( x ) = 3 x − 4 x 3 / 4 ; ( 0 , ∞ )

Solution Summary: The author explains that the function g(x) has no point of maxima and a absolute minima at x=1.

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To calculate: The locations of absolute extrema of the function given below on the given interval:

g(x)=3x−4x3/4 ;(0,∞)

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Chapter 12 Solutions

The locations of absolute extrema of the function given below on the given interval: g ( x ) = 3 x − 4 x 3 / 4 ; ( 0 , ∞ )

Solution Summary: The author explains that the function g(x) has no point of maxima and a absolute minima at x=1.

Concept explainers

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To calculate: The locations of absolute extrema of the function given below on the given interval: g(x)=3x−4x3/4 ;(0,∞)

Want to see the full answer?

Chapter 12 Solutions

To calculate: The locations of absolute extrema of the function given below on the given interval:

g(x)=3x−4x3/4 ;(0,∞)