A particle moves on the x-axis in such a way that its position at time t, t>0, is given by x(t) = (ln x)^2. At what value of t does the velocity of the particle attain maximum?
Suppose a population of bears grows according to the logistic differential equation
dP/dt = 2P - 0.01P^2
where P is the number of bears at time t in years. Which of the following statements are true?
I. The growth rate of the bear population is greatest at 100
II. If P > 200, the population of bears is decreasing.
III. lim t -> inf P(t) = 200
A conical tank is being filled with water at the rate of 16 ft^3/min. The rate of change of the depth of the water is 4 times the rate of change of the radius of the water surface. At the moment when the depth is 8ft and the radius of the surface is 2ft, the area of the surface is changing at what rate?
Out of 28 different questions, I couldn't figure out how to do these.
Thanks for your help