Question

A population of flies is growing in a large container. The number of flies P (in hundreds) after t weeks is given by P= 12t^2-t^4+5. When does the population stop growing? Over what time Intervals is the rate of population growth positive? Negative?

Answer 1

If you take the first derivative of the function and set it equal to zero, you find the critical points are 0 and + or - sqrt6). Checking the regions surrounding the critical points in the derivative gives an increasing function when positive and decreasing when negative. Since we are working with a function of time, the negative values are not relevant.

Answer 2

Let me know what you get.