Let define a curve for .

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Let

r=1+\cos\theta

define a curve for

0\le\theta\le2\pi

. (a) Express

x

and

y

in terms of

\theta

for this curve. (b) Compute

\dfrac{dy}{dx}

as a function of

\theta

. (c) Determine all values of

\theta

[0,2\pi]

at which the curve has a horizontal tangent line and all values at which it has a vertical tangent line. (d) Evaluate

\dfrac{d^2y}{dx^2}

at each

\theta

found in part (c) to classify the concavity of the curve at those tangent points.