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Calculus/Calculus AB

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Expert: - 1/1/2011


Question
Consider the curve defined by the equation y + cosy = x + 1 for 0<=y<=2pi.  Write an equation for each vertical tangent to the curve.  

I have y = pi/2, but isn't that a horizontal tangent?

Answer
Hello Mike,

We need to find where dy/dx is undefined. Differentiating gives:
y'-y'sin(y)=1 ==> y'(1-sin(y))=1 ==> y'=1/(1-sin(y))

So, y' is undefined where sin(y)=1. On the interval 0<=y<=2pi that
occurs only at pi/2.

Now find the x-value corresponding to y=pi/2:
pi/2+cos(pi/2)=x+1 ==> x=pi/2-1

Thus, the equation of the vertical tangent is x=pi/2 - 1

Abe

Calculus

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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