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# Marine biologists have determined that when a shark ISBN: 9781285740621 127

## Solution for problem 2 Chapter 14

Calculus | 8th Edition

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Problem 2

Marine biologists have determined that when a shark detects the presence of blood in the water, it will swim in the direction in which the concentration of the blood increases most rapidly. Based on certain tests, the concentration of blood (in parts per million) at a point Psx, yd on the surface of seawater is approximated by Csx, yd e2sx 212y 2 dy10 4 where x and y are measured in meters in a rectangular coordinate system with the blood source at the origin. (a) Identify the level curves of the concentration function and sketch several members of this family together with a path that a shark will follow to the source. (b) Suppose a shark is at the point sx0, y0d when it first detects the presence of blood in the water. Find an equation of the sharks path by setting up and solving a differential equation.

Step-by-Step Solution:
Step 1 of 3

Overview week of 9/12/16 3.3 Rules of Differentiation Power of X: d n (n­1) Power Rule: / Xdx= nX Quotient Rule: / f(x)/g(x) = [(f(x) * g(x)) – (f(x) * g(x))] / [g(x)] 2 dx Product Rule: / [dxx) * g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Chain Rule: / [dxg(x))] = [f(g(x))]’ * g’(x) Constant Multiple: Power rule d /dx(cf(x)) = c * f ’(x) 3.4 Product and Quotient Rules Product Rule: While [f(x) +/­ g(x)]’ = f ‘(x) +/­ g’(x), The same does not apply to multiplication And division. [f(x)g(x)] ≠ f ‘(x) * g’(x) Instead: [f(x)g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Products of multiple functions: (fg)’ = f’g + fg’ (fgh)’ = f’gh + fg’h + fgh’ (fghi)’ = f’ghi + fg’hi + fgh’i + fghi’

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##### ISBN: 9781285740621

The full step-by-step solution to problem: 2 from chapter: 14 was answered by , our top Calculus solution expert on 11/10/17, 05:27PM. Since the solution to 2 from 14 chapter was answered, more than 519 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Blood, concentration, shark, presence, Water. This expansive textbook survival guide covers 16 chapters, and 250 solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9781285740621. The answer to “Marine biologists have determined that when a shark detects the presence of blood in the water, it will swim in the direction in which the concentration of the blood increases most rapidly. Based on certain tests, the concentration of blood (in parts per million) at a point Psx, yd on the surface of seawater is approximated by Csx, yd e2sx 212y 2 dy10 4 where x and y are measured in meters in a rectangular coordinate system with the blood source at the origin. (a) Identify the level curves of the concentration function and sketch several members of this family together with a path that a shark will follow to the source. (b) Suppose a shark is at the point sx0, y0d when it first detects the presence of blood in the water. Find an equation of the sharks path by setting up and solving a differential equation.” is broken down into a number of easy to follow steps, and 148 words.

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Marine biologists have determined that when a shark