Explanation Given: The provided function is: f ( x ) = x + 4 x 2 . 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 If the f ( x ) = u ( x ) v ( x ) , if all indicated derivatives exist, and v ( x ) ≠ 0 , then the derivative of the function f ( x ) by division rule is, f ′ ( x ) = v ( x ) ⋅ u ′ ( x ) − u ( x ) ⋅ v ′ ( x ) ( v ( x ) ) 2 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 following expression. f ( x ) = x + 4 x 2 …… (1) Differentiate the above expression

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Chapter 12.2, Problem 44E

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To calculate: The critical numbers of f(x)=x+4x2. Then use the second derivative to check whether the critical number leads to maxima or minima.

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Chapter 12.2, Problem 43E

Chapter 12.2, Problem 45E

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Chapter 12 Solutions

EBK MATHEMATICS WITH APPLICATIONS IN TH

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 critical numbers of f ( x ) = x + 4 x 2 . Then use the second derivative to check whether the critical number leads to maxima or minima .

Solution Summary: The author explains how to calculate the critical numbers of f(x) and the second derivative to check whether it leads to maxima or minima.

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To calculate: The critical numbers of f(x)=x+4x2. Then use the second derivative to check whether the critical number leads to maxima or minima.

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