To determine To calculate: The interval when the sales are decreasing for the sales function, S ( x ) = x 3 − 21 x 2 + 120 x . Explanation Given: The sales function is: S ( x ) = x 3 − 21 x 2 + 120 x Formula used: The power formula of differentiation: d d x x n = n x n − 1 Calculation: Consider the sales function, S ( x ) = x 3 − 21 x 2 + 120 x In order to find the intervals, calculate S ′ ( x ) . Then, S ′ ( x ) = d d x ( x 3 ) − 21 d d x ( x 2 ) + 120 d d x ( x ) = ( 3 x 2 ) − 21 ⋅ ( 2 x ) + 120 ⋅ ( 1 ) = 3 x 2 − 42 x + 120 = x 2 − 14 x + 40 Now, equate S ′ ( x ) to 0. x 2 − 14 x + 40 = 0 ( x − 10 ) ( x − 4 ) = 0 x = 4 , 10 Since the critical points are 4 and 10. So, the graph changes direction at x = 4 and x = 10

12th Edition

ISBN: 9780135335215

Author: Lial

Publisher: PEARSON

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Chapter 12.1, Problem 9CP

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To calculate: The interval when the sales are decreasing for the sales function,

S(x)=x3−21x2+120x.

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Chapter 12.1, Problem 8CP

Chapter 12.1, Problem 1E

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Chapter 12 Solutions

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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 interval when the sales are decreasing for the sales function, S ( x ) = x 3 − 21 x 2 + 120 x .

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To calculate: The interval when the sales are decreasing for the sales function, S(x)=x3−21x2+120x.

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Chapter 12 Solutions

To calculate: The interval when the sales are decreasing for the sales function,

S(x)=x3−21x2+120x.