To determine To calculate: The water temperature that produces the maximum number of salmon swimming upstream. Explanation Given: The provided function: s ( x ) = − x 3 + 3 x 2 + 400 x + 5000 Where; x lies in the interval [ 6 , 20 ] and it represents the temperature of the water in degree Celsius. Formula used: The derivative property as; d d x ( x n ) = n x n − 1 And According to the first derivative test, if 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 maxima at c . 2. For f ′ ( a ) < 0 and f ′ ( b ) > 0 , there will be a local minima at c . 3. There will be no local extrema when f ′ ( a ) and f ′ ( b ) are either both positive or both negative Calculation: Consider the provided function: s ( x ) = − x 3 + 3 x 2 + 400 x + 5000 To get the water temperature that produces the maximum number of saloon put s ′ ( x ) = 0 Use derivative formulae in the above function which is: d d x ( x n ) = n x n − 1 and d d x ( c ) = 0 Where; c constant value and its derivative is zero then, d d x ( − x 3 + 3 x 2 + 400 x + 5000 ) = 3 ( − x 2 ) + 6 x + 400 = − 3 x 2 + 6 x + 400 Now put s ′ ( x ) = 0 .That is, − 3 x 2 + 6 x + 400 = 0 3 x 2 − 6 x − 400 = 0 The above expression is quadratic equation so use quadratic formulae that are written below: x = − b ± b 2 − 4 ⋅ a ⋅ c 2 a The general form of a quadratic equation is as follows: f ( x ) = a x 2 + b x + c In which a , b , c are real number and a ≠ 0 Compare given quadratic function with the general form of quadratic function then the resulting value will be written below: a = 3 , b = − 6 , c = − 400 Then, x = − b ± b 2 − 4 ⋅ a ⋅ c 2 a = − ( − 6 ) ± ( − 6 ) 2 − 4 ⋅ 3 ⋅ ( − 400 ) 2 ⋅ 3 = 6 ± 36 + 4800 6 = 6 ± 4836 6 Further solve and get, x = 6 ± 4836 6 = 6 ± 69

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

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

See similar textbooks

Concept explainers

Roots

Videos

Question

Chapter 12.1, Problem 59E

To determine

To calculate: The water temperature that produces the maximum number of salmon swimming upstream.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.1, Problem 55E

Chapter 12.1, Problem 56E

Students have asked these similar questions

Task number: A1.1, A1.7 Topic: Celestial Navigation, Compass - Magnetic and Gyro Activ Determine compass error (magnetic and gyro) using azimuth choosing a suitable celestial body (Sun/ Stars/ Planets/ Moon). Apply variation to find the deviation of the magnetic compass. Minimum number of times that activity should be recorded: 6 (2 each phase) Sample calculation (Azimuth- Planets): On 06th May 2006 at 22h20m 10s UTC, a vessel in position 48°00'N 050°00'E observed Mars bearing 327° by compass. Find the compass error. If variation was 4.0° East, calculate the deviation. GHA Mars (06d 22h): Increment (20m 10s): 089° 55.7' 005° 02.5' v (0.9): (+) 00.3' GHA Mars: 094° 58.5' Longitude (E): (+) 050° 00.0' (plus- since longitude is easterly) LHA Mars: 144° 58.5' Declination (06d 22h): d (0.2): N 024° 18.6' (-) 00.1' Declination Mars: N 024° 18.5' P=144° 58.5' (If LHA<180°, P=LHA) A Tan Latitude/ Tan P A Tan 48° 00' Tan 144° 58.5' A = 1.584646985 N (A is named opposite to latitude, except when…

Activ Determine compass error using amplitude (Sun). Minimum number of times that activity should be performed: 3 (1 each phase) Sample calculation (Amplitude- Sun): On 07th May 2006 at Sunset, a vessel in position 10°00'N 010°00'W observed the Sun bearing 288° by compass. Find the compass error. LMT Sunset: LIT: (+) 00d 07d 18h 00h 13m 40m UTC Sunset: 07d 18h 53m (added- since longitude is westerly) Declination (07d 18h): N 016° 55.5' d (0.7): (+) 00.6' Declination Sun: N 016° 56.1' Sin Amplitude = Sin Declination/Cos Latitude = Sin 016°56.1'/ Cos 10°00' = 0.295780189 Amplitude=W17.2N (The prefix of amplitude is named easterly if body is rising, and westerly if body is setting. The suffix is named same as declination) True Bearing=287.2° Compass Bearing= 288.0° Compass Error = 0.8° West

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

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.