Emanuel F.

asked • 02/27/20

Find the values of x on the curve y = cos x/(2 + sin x) at which the tangent is horizontal. (Let n be an integer. Enter your answers as a comma-separated list.)

1 Expert Answer

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Matthew S. answered • 02/27/20

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PhD in Mathematics with extensive experience teaching Calculus

Emanuel F.

Sorry, disregard the last part, that was added by accident
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02/28/20

Matthew S.

dy/dx = [-sinx * (2 + sinx) - cos^2x]/(2+sinx)^2. Set numerator equal to 0 to find critical values. Since sin^2(x) + cos^2(x) = 1, numerator simplifies to -1 - 2sinx. Critical value when sinx = -1/2. Occurs when x = 7pi/6 + any multiple of 2pi or when x = 11pi/6 + any multiple of 2pi.
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02/28/20

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