To maximize a function we usually need to look at the zeros of the differentiation of the function.
We will find that we have a local maximum in February
We want to find a local maximum for the equation:
S(t) = t^4 - 8*t^3 + 22*t^2 - 24*t + 9
To see this we need to derivate the function, we will get:
S'(t) = 4*t^3 - 3*8*t^2 + 2*22*t - 24
= 4*t^3 - 24*t^2 + 44*t - 24
The graph of this can be seen in the image below.
Remember that a derivate tells us how the original function changes with the variable. So if the derivate is negative in a given interval, then the function decreases in that interval.
Thus, in the graph we can see that the line is positive in the interval between 1 and 2, so in that interval the function was increasing, then when you get to t = 2 you have an x-intercept, thus the function stops increasing and starts decreasing.
Then we have the local maximum at t = 2, which is Ferbruary
The correct option is February
If you want to learn more, you can read:
https://brainly.com/question/20394217
