Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.2 Linear and Quadratic Functions - Exercises - Page 19: 46


The largest frequency of heterozygous carriers occurs when $p=0.5$.

Work Step by Step

The frequency of heterozygous carriers is $y=2p(1-p)$, which is an inverted parabola $(\cap-\text{shaped})$ curve. The curve is symmetric about the vertical line passing through the maximum point. The y-coordinate is $0$ when $2p(1-p)=0$, or, $p(1-p)=0$, which gives $p=0$ and $p=1$, which are the roots. The line of symmetry passes from the mid of the roots, i.e., $p=0.5$ is the line of symmetry. Now, the maximum point lies on the line of symmetry, so, the largest frequency of heterozygous carriers occurs when $p=0.5$.
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