Math CentralQuandaries & Queries

Question from Paulina:

Find the rate of change of the distance between the origin and a moving point on the graph of y=x^2 +1 if dx/dt=2 centimeters per second

Hi Paulina,

Let $P(x, y)$ be a point on the graph of $y = x^2 + 1$, let $O$ be the origin and $Q$ the point $(x, 0).$


Since $P$ is on the graph we know that $y = x^2 + 1$ and hence the distance from $Q$ to $P$ is $y = x^2 + 1.$ Use Pythagoras Theorem to write $D$ the distance from $O$ to $P$ as a function of $x.$ Differentiate $D$ with respect to $t.$



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