A point travels on the parabola defined implicitly by

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

x^{2}-y+1=0

. At the instant when the point has coordinates

(2,5)

, the

y

-coordinate is decreasing at a rate of

4\text{ units s}^{-1}

. (a) Determine

\dfrac{dx}{dt}

at that instant. (b) Find the rate of change of the distance from the point to the origin at that same moment.