Explanation Given: A biologist has found that the percentage of selenium in the soil x months after the flushing begins is given by: f ( x ) = x 2 + 36 2 x ; ( 1 ≤ x ≤ 12 ) Formula used: The power, and quotient formula of differentiation: d d x x n = n x n − 1 d d x ( f ( x ) g ( x ) ) = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) ( g ( x ) ) 2 And According to the first derivative test, c is the only critical number of the given function for an interval [ a , b ] such that a < c < b . Consider, f is differential for every value of x in the interval except at x = c . 1. For f ′ ( a ) > 0 and f ′ ( b ) < 0 , there will be a local maximum at c . 2. For f ′ ( a ) < 0 and f ′ ( b ) > 0 , there will be a local minimum at c . 3. There will be no local extrema when f ′ ( a ) and f ′ ( b ) are either both positive or both negative Calculation: Determine the critical numbers by finding the derivative of the provided function: f ( x ) = x 2 + 36 2 x The derivative of the function f ( x ) : f ′ ( x ) = d d x ( x 2 + 36 2 x ) = (<

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

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Chapter 12.1, Problem 66E

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To calculate: The time when the selenium will be reduced to a minimum and also, its minimum percentage if a biologist has found that the percentage of selenium in the soil x months after the flushing begins is given by:

f(x)=x2+362x;(1≤x≤12)

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Chapter 12.1, Problem 65E

Chapter 12.1, Problem 68E

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Chapter 12 Solutions

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

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 time when the selenium will be reduced to a minimum and also, its minimum percentage if a biologist has found that the percentage of selenium in the soil x months after the flushing begins is given by: f ( x ) = x 2 + 36 2 x ; ( 1 ≤ x ≤ 12 )

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To calculate: The time when the selenium will be reduced to a minimum and also, its minimum percentage if a biologist has found that the percentage of selenium in the soil x months after the flushing begins is given by: f(x)=x2+362x;(1≤x≤12)

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Chapter 12 Solutions

To calculate: The time when the selenium will be reduced to a minimum and also, its minimum percentage if a biologist has found that the percentage of selenium in the soil x months after the flushing begins is given by:

f(x)=x2+362x;(1≤x≤12)