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.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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