The distance between the origin and a moving point

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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
y=x^2+2

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.

Penny

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