A 10-ft ladder rests against a vertical wall

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A 10-ft ladder rests against a vertical wall. The bottom of the ladder slides away from the wall at a constant rate of 3 ft/s. Let

x

denote the horizontal distance from the foot of the ladder to the wall and

y

the vertical height of the ladder’s top on the wall. Which of the following correctly describes the signs of

dx/dt

and

dy/dt

at that instant? (a)

dx/dt<0 \text{ and } dy/dt>0

(b)

dx/dt>0 \text{ and } dy/dt<0

(c)

dx/dt>0 \text{ and } dy/dt>0

(d)

dx/dt<0 \text{ and } dy/dt<0