Related Rates
A ladder 10 meters long is leaning against a vertical wall, with its other end on the ground. The top end is sliding down the wall. When the top is 6 meters from the ground, it is sliding at 2 m/s. How fast is the bottom moving at this instant?
3/2 m/s or 1.5 m/s
Find the average velocity for an object during the first 4 seconds if the object's position is given by x(t) = -4.9t2+500
-19.6
Gutterez plans to build two side by side identical rectangular pens for his pigs that will enclose a total area of 216 ft2. What is the minimum length of fencing he will need?
18 feet by 12 feet (60 total feet)
y = 4sin3(2x3)
Find dy/dx
72x2sin2(2x3)cos(2x3)
Two cars leave from the same position at the same time. One travels due North at 30 mph. The other travels due East at 40 mph. At what rate is the distance between them changing after 2 hours?
50 mph
Where does the function f(x) = 3x2-12x+1 satisfy Rolle's Theorem on the interval [0,4]?
c=2
Camryn wants to design an open-top box having a square base and a surface area of 80 square inches. What is the maximum volume?
68.853 in3
Find the equation of the tangent line of
y=tan x at x = pi/6
y - sqrt3/3 = 4/3(x-pi/6)
Air is escaping from a spherical balloon at a rate of 2 cubic cm per minute. How fast is the surface area shrinking when the radius is 1 cm? (V = 4/3 pi r3 and SA = 4 pi r2)
-4 square cm per min
Use MVT to show where the instantaneous velocity of an object equals the average velocity of the first 4 seconds, when the position of the object is given by x(t) = -4.9t2+500
2 seconds
f(x) = (2x)/(x2+1) on the interval [-2,2]
Find the absolute max and min
Max is 1 @ x = 1
Min is -1 @ x = -1
The position of a particle moving along the x-axis is x(t) = sin(2t).
What is the acceleration of the particle at t = pi
0