# Polar Curve and maximum width

Find the maximum width of the petal of the four-leaved rose $r = \cos2\theta$, which lies along the x-axis

Here is the solution

Can someone tell me how on earth did the solution come up with the first step?

The statement "The maximum width of the petal of the rose which lies on along the x-axis is twice the largest y-value of the curve on the interval..."

Maybe the curve I sketched wasn't great, but I did it again on Mathematica and I still couldn't see how they notice this "ingenuous" subtle observation.

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$r = \cos\theta$ is a circle; did you forget to include part of the equation for the four-leaved rose? –  amWhy Dec 27 '12 at 21:03

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