Math CentralQuandaries & Queries


Question from Norma, a student:

I am having problems with this question
find the rate of change of the distance between the origin and a moving point on the graph of the function below if dx/dt=5 cm/sec

Hi Norma,

The distance from the origin to a point (x, y) in the plane is S = √[x2 + y2] cm. If (x , y) is on the curve y = x2 + 2 then this distance is S = √[x2 + (x2 + 2)2] cm. Simplify this expression.

Since the point is moving along the curve S is a function of time t where t is measured in seconds. Differentiate S with respect to t and then substitute dx/dt=5 cm/sec.


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