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 For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.1: Antiderivatives

Problem 45E

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