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A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a towrn 11 miles down the shore from P in the least time? Let a be the distance between point P and where the boat lands on the lake shore. (A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance a. T(x) = (B) What is the distance a = c that minimizes the travel time? Note: The answer to this problem requires that you enter the correct units. C = (C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units. ........ The least travel time is (D) Recall that the second derivative test says that if T'(c) = 0 and T"(c) > 0, then T has a local minimum at c. What is T"(c)? T"(c) =

A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a towrn 11 miles down the shore from P in the least time? Let a be the distance between point P and where the boat lands on the lake shore. (A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance a. T(x) = (B) What is the distance a = c that minimizes the travel time? Note: The answer to this problem requires that you enter the correct units. C = (C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units. ........ The least travel time is (D) Recall that the second derivative test says that if T'(c) = 0 and T"(c) > 0, then T has a local minimum at c. What is T"(c)? T"(c) =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 11 miles down the shore from P in the least time? Let a be the distance between point P and where the boat lands on the lake shore. (A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance a. T(a) = %3D (B) What is the distance x = c that minimizes the travel time? Note: The answer to this problem requires that you enter the correct units. C = (C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units. The least travel time is (D) Recall that the second derivative test says that if T'(c) = 0 and T"(c) > 0, then T has a local minimum at c. What is T"(c)? T"(c) =
Transcribed Image Text:A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 11 miles down the shore from P in the least time? Let a be the distance between point P and where the boat lands on the lake shore. (A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance a. T(a) = %3D (B) What is the distance x = c that minimizes the travel time? Note: The answer to this problem requires that you enter the correct units. C = (C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units. The least travel time is (D) Recall that the second derivative test says that if T'(c) = 0 and T"(c) > 0, then T has a local minimum at c. What is T"(c)? T"(c) =
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