Explanation Given: The microbe concentration of Lake Tom depends on the oxygen concentration and it is expressed as, B ( x ) = x 3 − 7 x 2 − 160 x + 1800 , 0 ≤ x ≤ 20 Here, B ( x ) is the microbe concentration and x is the oxygen concentration. 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: For the extremum microbe concentration, the derivative of the microbe concentration would be zero. Recall the expression of microbe concentration. B ( x ) = x 3 − 7 x 2 − 160 x + 1800 …… (1) Differentiate the expression of microbe concentration with respect to x by using the power rule for derivative. B ′ ( x ) = 3 x 3 − 1 − 7 ( 2 x 2 − 1 ) − 160 ( 1 ) + 0 = 3 x 2 − 14 x − 160 …… (2) For the extremum microbe concentration, B ′ ( x ) = 0 . Substitute 0 for B ′ ( x ) . 3 x 2 − 14 x − 160 = 0 Simplify the equation. 3 x 2 − 30 x + 16 x − 160 = 0 3 x ( x − 10 ) + 16 ( x − 10 ) = 0 ( x − 10 ) ( 3 x + 16 ) = 0 Solve for x

Mathematics with Applications and Mylab Math with Pearson EText -- Title-Specific Access Card Package

12th Edition

ISBN: 9780134862668

Author: Lial, Margaret L.

Publisher: Pearson Education Canada

See similar textbooks

Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calcul…

Videos

Question

Chapter 12.1, Problem 55E

To determine

To calculate: The microbe concentration of Lake Tom depends on the oxygen concentration and it is expressed as B(x)=x3−7x2−160x+1800, 0≤x≤20. Here, B(x) is the microbe concentration and x is the oxygen concentration.

The oxygen concentration that will lead to the minimum microbe concentration.

The minimum microbe concentration.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.1, Problem 53E

Chapter 12.1, Problem 59E

Students have asked these similar questions

Please could you provide a step by step solutions to this question and explain every step.

Could you please help me with question 2bii. If possible could you explain how you found the bounds of the integral by using a graph of the region of integration. Thanks

Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b² = ab = ba = 0. (ii) a²=b, b² = ab = ba = 0. (iii) a²=b, b² = b, ab = ba = 0.

Chapter 12 Solutions

Mathematics with Applications and Mylab Math with Pearson EText -- Title-Specific Access Card Package

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Solution Summary: The author explains how the microbe concentration of Lake Tom depends on the oxygen concentration.

Concept explainers

Videos

Want to see the full answer?

Chapter 12 Solutions