1) If y = 2x3 - 4x and dx, dt equals 4 , find dy/ dt when x = 1.
2) The area A = πr^2 of a circular water ripple changes with the radius. At what rate does the area change with respect to the radius when r = 4ft?
3) A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x^2h cm^3. Find the rate at which the volume of the box is changing when the edge length of the base is 10 cm, the edge length of the base is increasing at a rate of 3 cm/min, the height of the box is 5 cm, and the height is decreasing at a rate of 1 cm/min.
4) The height of a cylinder with a fixed radius of 10 cm is increasing at the rate of 0.5 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 30cm.
Where are your attempts to do these? Where did you get stuck? I already took the subject, do not need practice. They are all really the same. For example the last one:
r = 10
V = pi r^2 h = 100pi h
100 pi is a constant so
dV/dt = 100 pi * dh/dt
or the second one (the first one has a typo)
dA/dt = dA/dr * dr/dt = 2 pi r * dr/dt
in other words the area increase is the circumference times dr
Deondre = James
Never would have guessed :)