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25+x + . Step 4 To find the least time differentiate T(x) with respect to x, T'(x)=- 3(2/25+x) 3(V25+x) finding critical points using T'(x)=0.

25+x + . Step 4 To find the least time differentiate T(x) with respect to x, T'(x)=- 3(2/25+x) 3(V25+x) finding critical points using T'(x)=0.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Step 4. Where did the 2x come from.
As the woman walks the distance of 11 -r miles with a speed of 4 miles per hour. Therefore, the time taken by the woman to walk is . Therefore, the time taken by a woman to arrive at a town 11 miles down the shore from point P is given by V25+x %3D Step 4 To find the least time differentiate T(x) with respect to x, 2x 3(2/25+x) i- T'(x)= finding critical points using T'(x)=0. ! = 0 3(V25+2?) Solving for x, 4x=3 (V25 + x?) 16x?=9(25 + x?) 16x=225 + 9x? 16x? – 9x2=225 7x=225 Therefore, x = 4 x 5. 67miles. Step 5 Again differentiating T'(x) with respect to x again. (V25+x?)1-x (V) 3(V3+2) T "(x)= 25+x-x? 3(V25+x2) 25 %3D 3(V25+x) 225 25 >0 Therefore, time will be minimum when x = 4 x 5. 67. Thuc the hestuill h11 reiles dewn the chore 米
Transcribed Image Text:As the woman walks the distance of 11 -r miles with a speed of 4 miles per hour. Therefore, the time taken by the woman to walk is . Therefore, the time taken by a woman to arrive at a town 11 miles down the shore from point P is given by V25+x %3D Step 4 To find the least time differentiate T(x) with respect to x, 2x 3(2/25+x) i- T'(x)= finding critical points using T'(x)=0. ! = 0 3(V25+2?) Solving for x, 4x=3 (V25 + x?) 16x?=9(25 + x?) 16x=225 + 9x? 16x? – 9x2=225 7x=225 Therefore, x = 4 x 5. 67miles. Step 5 Again differentiating T'(x) with respect to x again. (V25+x?)1-x (V) 3(V3+2) T "(x)= 25+x-x? 3(V25+x2) 25 %3D 3(V25+x) 225 25 >0 Therefore, time will be minimum when x = 4 x 5. 67. Thuc the hestuill h11 reiles dewn the chore 米
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