You titled this "Applications of derivatives". What is the derivative of p(t)? What does the derivative have to do with finding maximum values?I'm having trouble with the following problem: Epidemiologists have found a new communicable disease running rampant in a college. They estimate that t days after the disease is first observed in the community, the percent of the population infected by the disease is approximated by p(t)= (20 t^3-t^4)/1000. Also t is greater than or equal 0 and less than or equal to 20. After how many days is the percent of the population infected a maximum?
You titled this "Applications of derivatives". What is the derivative of p(t)? What does the derivative have to do with finding maximum values?
That is a polynomial: \(\displaystyle \frac{20}{1000}t^3- \frac{1}{1000}t^4= \frac{1}{50}t^3 - \frac{1}{1000}t^4\). The derivative of \(\displaystyle t^n\) is \(\displaystyle nt^{n-1}\).That's what I'm having the problem with, finding p'(t), I'm not sure if its because it is just a whole number in the denominator.