A 17-foot ladder is sliding down a wall at a rate of -5feet/sec. When the top of the ladder is 8 feet from the

Question

ground, how fast is the foot of the ladder sliding away from the wall (in feet/sec.)?

A rectangle is to be the inscribed between the parabola y=4-x^2 and the x-axis, with its base on the x-axis. A value of x that maximizes the area of the rectangle is?

Answer 1

Sketch the triangle, call vertical side v, horizontal side h. We know v² + h² = 17², so h² = 289 - v², h = √(289 - v²).

dh/dv = -2v / 2√(289 - v²) = -v / √(289 - v²), and
dh/dt = dh/dv • dv/dt

dv/dt = -5 when v = 8, so
dh/dt = -8/√(289 - 8²) • -5
dh/dt = 40/15 = 2 2/3 ft/s.

Answer 2

rate=distance/time