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3. Consider the function y = f(x) whose curve is given by the equation 2y² - 6 = y sin x for y > 0. dy y cos x (a) Show that = dx 4y - sin x (b) Write an equation for the line tangent to the curve at the point (0,√3). (c) For 0≤x≤ and y> 0, find the coordinates of the point where the line tangent to the curve is horizontal. (d) Determine whether f has a relative minimum, a relative maximum, or neither at the point found in part (c). Justify your answer.

3. Consider the function y = f(x) whose curve is given by the equation 2y² - 6 = y sin x for y > 0. dy y cos x (a) Show that = dx 4y - sin x (b) Write an equation for the line tangent to the curve at the point (0,√3). (c) For 0≤x≤ and y> 0, find the coordinates of the point where the line tangent to the curve is horizontal. (d) Determine whether f has a relative minimum, a relative maximum, or neither at the point found in part (c). Justify your answer.

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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Part d The point found in part c is (π/2 , 2)
3. Consider the function y = f(x) whose curve is given by the equation 2y² - 6 = y sin x for y> 0. dy y cos x dx 4y - sin x (b) Write an equation for the line tangent to the curve at the point (0, √3). (a) Show that (c) For 0≤x≤ and y> 0, find the coordinates of the point where the line tangent to the curve is horizontal. (d) Determine whether f has a relative minimum, a relative maximum, or neither at the point found in part (c). Justify your answer. Y cost 7 f(x) = 2y² - 6 = y sinx d) f(x)= -Sink Чу f'(x) = 4y+y¹-0 = y² sinx +y cos x f'(a) = (y 'cosx + y + - Sinx) (4 y-sin x)-(- ix) ²
Transcribed Image Text:3. Consider the function y = f(x) whose curve is given by the equation 2y² - 6 = y sin x for y> 0. dy y cos x dx 4y - sin x (b) Write an equation for the line tangent to the curve at the point (0, √3). (a) Show that (c) For 0≤x≤ and y> 0, find the coordinates of the point where the line tangent to the curve is horizontal. (d) Determine whether f has a relative minimum, a relative maximum, or neither at the point found in part (c). Justify your answer. Y cost 7 f(x) = 2y² - 6 = y sinx d) f(x)= -Sink Чу f'(x) = 4y+y¹-0 = y² sinx +y cos x f'(a) = (y 'cosx + y + - Sinx) (4 y-sin x)-(- ix) ²
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