Quandaries
and Queries 

Trying to solve a rate of change problem. Similar to one in the database Find the rate of change of the distance between the origin and a moving I am sending this for my daughter a senior taking high school calculus. I Frank 

Hi Frank, I sketched the curve and marked a point P on the curve with first coordinate x. Since the curve is
the point P has coordinates (x, x^{2} + 1). Let s(x) be the distance between the origin O and the point P then
x is a function of time t so s(x) is a function of time and you can differentiate s(x) with respect to t.
Substitute dx/dt = 2 centimeters per second and you have an expression that gives you the rate of change of the distance between the origin and an arbitrary point P on the curve. Penny 

